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51. Location and Strategies in Stackelberg Security Games with Risk Aversion

Author

Chicoisne, Renaud, Ordóñez, Fernando, Castro, Daniel, Département d'Informatique [Bruxelles] (ULB), Faculté des Sciences [Bruxelles] (ULB), Université libre de Bruxelles (ULB)-Université libre de Bruxelles (ULB), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Institut Supérieur d'Informatique, de Modélisation et de leurs Applications (ISIMA), Université Clermont Auvergne [2017-2020] (UCA [2017-2020]), Universidad de Chile = University of Chile [Santiago] (UCHILE), Accenture, and Chicoisne, Renaud

Subjects
Quantal Response, [INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO], Convex Optimization, Risk aversion, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Mixed-Integer Programming, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Stackelberg Security Games, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

In Stackelberg security games, a leader locates security resources to protect a set of targets from strategic adversaries that aim to attack these targets after observing the leader's strategy. In this setting, the leader decision problem is to optimize an uncertain reward that can take a discrete set of values with a probability distribution that depends on the decision variable. We show how diverse risk aversion models of the leader decision problem can be formulated as tractable optimization problems, such as imposing: a bound on the expected disutility, chance constraints, bounded distortion risk, first and second order stochastic dominance constraints, or optimizing a value-at-risk and conditional value-at-risk. We detail the resulting optimization problems and present computational results that show how the solution changes in two specific settings: 1) an entropic risk measure or value-at-risk minimization with a quantal response follower and 2) a prospect theory model with optimal follower response.

Published
2022

52. Advances in Sliding Mode Control of Earthquakes via Boundary Tracking of Wave and Diffusion PDEs

Author

Gutierrez-Oribio, Diego, Orlov, Yury, Stefanou, Ioannis, Plestan, Franck, Institut de Recherche en Génie Civil et Mécanique (GeM), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université - Institut Universitaire de Technologie Saint-Nazaire (Nantes Univ - IUT Saint-Nazaire), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - Ecole Polytechnique de l'Université de Nantes (Nantes Univ - EPUN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ), Centro de Investigacion Cientifica y de Education Superior de Ensenada [Mexico] (CICESE), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), and Stefanou, Ioannis

Subjects
[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; Two recent results on earthquake control are summarized. A simplified model of an earthquake phenomenon is addressed by means of a cascade system of a 1D wave equation, representing the fault slip and wave propagation, and a 1D diffusion equation, representing the actuator dynamics as a diffusion process. In order to avoid a fast slip (earthquakelike behaviour), the control is designed to follow a slow reference. The control strategies are presented separately for both Partial Differential Equations (PDEs). For the wave PDE, a homogeneous boundary tracking control is developed to achieve exponential Input to State Stability (eISS) of the error closedloop dynamics. For the diffusion PDE, Proportional Integral (PI) and a discontinuous integral term are coupled to exponentially stabilize the error origin despite model uncertainties and perturbations. Simulations are additionally conducted to support the robustness and stability properties of the proposed control algorithms, by separately, obtaining critical remarks that will lead to the design of the single control for the cascade system in a future stage.

Published
2022

53. Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces

Author

Bonnet, Benoît, Frankowska, Hélène, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Bonnet-Weill, Benoît

Subjects
Optimization and Control (math.OC), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, FOS: Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering, Mathematics - Optimization and Control
Abstract

In this article, we prove a general viability theorem for continuity inclusions in Wasserstein spaces, and provide an application thereof to the existence of exponentially stable trajectories obtained via the second method of Lyapunov.

Published
2022

54. Dissipative Systems Analysis and Control. Theory and Applications: Erratum/Addendum. Springer Nature Switzerland AG, Communications and Control Engineering, Third uncorrected Edition, 2020

Author

Brogliato, Bernard, Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and Brogliato, Bernard

Subjects
[SPI.AUTO] Engineering Sciences [physics]/Automatic, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

I will be glad to receive any comment which helps me to improve this Erratum/Addendum.; This Erratum/Addendum concerns the third edition of the book, uncorrected version, published in 2020.

Published
2022

55. Fast Stochastic Composite Minimization and an Accelerated Frank-Wolfe Algorithm under Parallelization

Author

Dubois-Taine, Benjamin, Bach, Francis, Berthet, Quentin, Taylor, Adrien, Département d'informatique - ENS Paris (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL), Centre National de la Recherche Scientifique (CNRS), Statistical Machine Learning and Parsimony (SIERRA), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), Google Brain, Paris, The authors acknowledge support from the European Research Council (grant SEQUOIA 724063). This work was funded in part by the french government under management of Agence Nationale de la recherche as part of the 'Investissements d’avenir' program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute)., ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), European Project: 724063,ERC-2016-COG,SEQUOIA(2017), Dubois-Taine, Benjamin, PaRis Artificial Intelligence Research InstitutE - - PRAIRIE2019 - ANR-19-P3IA-0001 - P3IA - VALID, and Robust algorithms for learning from modern data - SEQUOIA - - ERC-2016-COG2017-09-01 - 2018-11-30 - 724063 - VALID

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Optimization and Control (math.OC), FOS: Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control, Machine Learning (cs.LG)
Abstract

We consider the problem of minimizing the sum of two convex functions. One of those functions has Lipschitz-continuous gradients, and can be accessed via stochastic oracles, whereas the other is "simple". We provide a Bregman-type algorithm with accelerated convergence in function values to a ball containing the minimum. The radius of this ball depends on problem-dependent constants, including the variance of the stochastic oracle. We further show that this algorithmic setup naturally leads to a variant of Frank-Wolfe achieving acceleration under parallelization. More precisely, when minimizing a smooth convex function on a bounded domain, we show that one can achieve an $\epsilon$ primal-dual gap (in expectation) in $\tilde{O}(1/ \sqrt{\epsilon})$ iterations, by only accessing gradients of the original function and a linear maximization oracle with $O(1/\sqrt{\epsilon})$ computing units in parallel. We illustrate this fast convergence on synthetic numerical experiments.

Published
2022

56. Screen & Relax: Accélérer la résolution du problème 'Elastic-Net' par identification du support de la solution

Author

Theo Guyard, Cédric Herzet, Clément Elvira, Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA), SIMulation pARTiculaire de Modèles Stochastiques (SIMSMART), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut d'Électronique et des Technologies du numéRique (IETR), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), Guyard, Theo, and ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011)

Subjects
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

In this paper, we propose a procedure to accelerate the resolution of the well-known Elastic-Net problem. Our procedure is based on the partial identification of the solution support and the reformulation of the original problem as a problem of reduced dimension. The support identification leverages the novel concept of “relaxing” that can be viewed as a dual approach to the popular “screening“ methodology., Dans cet article, nous proposons une procédure pour accélérer la résolution du problème "Elastic-Net". Notre méthode est basée sur l'identification partielle du support de la solution, permettant une reformulation du problème original en un problème de dimension réduite. Cette identification s'appuie sur le concept de "relaxing" qui peut être considéré comme une approche duale de la méthodologie de "screening".

Published
2022

57. Holistic vision of Inverse Optimal Control

Author

Colombel, Jessica, Daney, David, Charpillet, François, Faculté des Sciences et Technologies [Université de Lorraine] (FST ), Université de Lorraine (UL), Lifelong Autonomy and interaction skills for Robots in a Sensing ENvironment (LARSEN), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Complex Systems, Artificial Intelligence & Robotics (LORIA - AIS), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Augmenting human comfort in the factory using cobots (AUCTUS), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Polytechnique de Bordeaux (Bordeaux INP), and Colombel, Jessica

Subjects
Identification, Inverse Optimal Control, [INFO.INFO-RB] Computer Science [cs]/Robotics [cs.RO], [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Human Motion Analysis, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

Inverse Optimal Control (IOC) is a problem that exists in many fields. In the context of human motion analysis, many methods for solving this problem have been proposed. This paper presents the Projected Inverse Optimal Control (PIOC) approach which puts forward a simple and complete vision of the problem. PIOC is composed of several independent elements allowing to cover problems of dimensioning, measurement noise and reliability of solution. The first element is the parameterization of the data, allowing to reduce the dimensions of the problem. The second element corresponds to the decoupling of the conditions including the conditions of identifiability of the parameters, singularity of the problem and feasibility of the solution. The last element refers to the choice of solution. We show with this approach that the classical solution methods are in fact projections in the space of trajectories. PIOC also allows us to propose a simple algorithm for the choice of basis, a recurrent problem in IOC

Published
2022

58. Les grandes matrices aléatoires : un aperçu historique

Author

Hachem, Walid, Laboratoire d'Informatique Gaspard-Monge (LIGM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), and Hachem, Walid

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; Cet article est une présentation historique très succincte de la théorie des grandes matrices aléatoires et de ses applications en traitement du signal, en communications numériques et en apprentissage statistique.

Published
2022

59. « Approximate Message Passing » et solutions de grands systèmes dynamiques écologiques de Lotka-Volterra

Author

Hachem, Walid, Najim, Jamal, Laboratoire d'Informatique Gaspard-Monge (LIGM), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, and Hachem, Walid

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; -Les systèmes dynamiques d'interaction écologique mettant en jeu n espèces vivantes sont couramment décrits par une équation différentielle, stochastique ou non, dite de Lotka-Volterra (L.-V.). Dans cette équation, l'objet important est la matrice aléatoire n × n des interactions alimentaires entre les espèces au sein de l'écosystème étudié. L'existence et la pré compacité de la solution d'une équation de L.-V. dépend étroitement d'un certain paramètre spectral associé à cette matrice. Dans cet article, nous étudions la convergence de ce paramètre dans le régime des grandes dimensions. Nous obtenons des résultats partiels grâce à la technique d'« Approximate Message Passing » issue de la physique statistique, rendue rigoureuse par Montanari et ses collègues et largement utilisée en traitement du signal et en apprentissage.

Published
2022

60. Small-time bilinear control of Schrödinger equations with application to rotating linear molecules

Author

Chambrion, Thomas, Pozzoli, Eugenio, Pozzoli, Eugenio, Contrôle quantique : systèmes d'EDPs et applications à l'IRM - - QUACO2017 - ANR-17-CE40-0007 - AAPG2017 - VALID, and Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité - - EIPHI2017 - ANR-17-EURE-0002 - EURE - VALID

Subjects
FOS: Physical sciences, Schrödinger equation, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Mathematical Physics (math-ph), infinite-dimensional systems, Optimization and Control (math.OC), Control and Systems Engineering, bilinear systems, FOS: Mathematics, linear molecule, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Electrical and Electronic Engineering, Quantum Physics (quant-ph), small-time controllability, [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph], Analysis of PDEs (math.AP)
Abstract

In [14] Duca and Nersesyan proved a small-time controllability property of nonlinear Schrödinger equations on a d-dimensional torus $\mathbb{T}^d$. In this paper we study a similar property, in the linear setting, starting from a closed Riemannian manifold. We then focus on the 2-dimensional sphere $S^2$, which models the bilinear control of a rotating linear top: as a corollary, we obtain the approximate controllability in arbitrarily small times among particular eigenfunctions of the Laplacian of $S^2$., 10 pages, 1 figure

Published
2023

61. Homotopic approach for turnpike and singularly perturbed optimal control problems

Author

Olivier Cots, Boris Wembe, Joseph Gergaud, Cots, Olivier, Algorithmes Parallèles et Optimisation (IRIT-APO), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, and Institut National Polytechnique (Toulouse) (Toulouse INP)

Subjects
T57-57.97, Applied mathematics. Quantitative methods, Computer science, Property (programming), Propriété Turnpike, Turnpike property, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Resolution (logic), 16. Peace & justice, Optimal control, Méthode homotopique, Set (abstract data type), Continuation, QA1-939, Contrôle optimal, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Singular perturbation, Link (knot theory), Control (linguistics), Mathematics, Perturbations singulières, Homotopic method
Abstract

The first aim of this article is to present the link between the turnpike property and the singular perturbations theory: the first one being a particular case of the second one. Then, thanks to this link, we set up a new framework based on continuation methods for the resolution of singularly perturbed optimal control problems. We consider first the turnpike case, then, we generalize the approach to general control problems with singular perturbations (that is with fast but also slow variables). We illustrate each step with an example., Dans cet article nous présentons le lien entre les points de vue turnpike et perturbations singulières en contrôle optimal en montrant notamment que le premier est un cas particulier du second. Ce lien important nous permet de mettre sur pieds une nouvelle approche de résolution numérique, basée sur les méthodes homotopiques, des problèmes de contrôle optimal perturbés singulièrement. Tout d'abord on s'intéresse aux cas turnpike, puis on généralise l'approche au cas perturbations singulières (marqués par la présence de variables lentes); chaque partie étant illustrée par un exemple.

Published
2021

62. Region-free Safe Screening Tests for l1-penalized Convex Problems

Author

Herzet, Cédric, Elvira, Clément, Dang, Hong-Phuong, SIMulation pARTiculaire de Modèles Stochastiques (SIMSMART), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut de Recherche Mathématique de Rennes (IRMAR), Institut d'Électronique et des Technologies du numéRique (IETR), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), Laboratoire de Traitement de l'Information Medicale (LaTIM), Université de Brest (UBO)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre Hospitalier Régional Universitaire de Brest (CHRU Brest)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Brestois Santé Agro Matière (IBSAM), Université de Brest (UBO), Elvira, Clément, ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Nantes Université - pôle Sciences et technologie

Subjects
safe screening, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], sparsity, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], convex problem, [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; We address the problem of safe screening for l1-penalized convex regression/classification problems, i.e., the identification of zero coordinates of the solutions. Unlike previous contributions of the literature, we propose a screening methodology which does not require the knowledge of a so-called "safe region". Our approach does not rely on any other assumption than convexity (in particular, no strong-convexity hypothesis is needed) and therefore applies to a wide family of convex problems. When the Fenchel conjugate of the data-fidelity term is strongly convex, we show that the popular "GAP sphere test" proposed by Fercoq et al. can be recovered as a particular case of our methodology (up to a minor modification). We illustrate numerically the performance of our procedure on the "sparse support vector machine classification" problem.

Published
2022

63. High-accuracy computation of rolling friction contact problems

Author

Acary, Vincent, Armand, Paul, Nguyen, Hoang Minh, Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and NGUYEN, Hoang Minh

Subjects
[PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], Nesterov and Todd scaling, rolling friction contact, Jordan algebra, [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], second-order cone optimization, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], optimization
Abstract

Our aim is to perform numerical solutions of an optimization model derived from the problem of unilateral contact between solid bodies with rolling friction. The model is an optimization problem with a strictly convex quadratic objective function and a second-order cone of constraints that is not self-dual. The solver is an implementation of a primal-dual interior-point algorithm with the predictor-corrector scheme of Mehrotra extended to second-order cone problem. We focused on the analysis of the limits of numerical computation and propose some treatments to achieve optimal solutions with ten significant digits precision.

Published
2022

64. Learning with Combinatorial Optimization Layers: a Probabilistic Approach

Author

Dalle, Guillaume, Baty, Léo, Bouvier, Louis, Parmentier, Axel, and Dalle, Guillaume

Subjects
graphs, FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Machine Learning (stat.ML), automatic differentiation, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG), machine learning, Optimization and Control (math.OC), Statistics - Machine Learning, Julia programming language, FOS: Mathematics, combinatorial optimization, Mathematics - Optimization and Control
Abstract

Combinatorial optimization (CO) layers in machine learning (ML) pipelines are a powerful tool to tackle data-driven decision tasks, but they come with two main challenges. First, the solution of a CO problem often behaves as a piecewise constant function of its objective parameters. Given that ML pipelines are typically trained using stochastic gradient descent, the absence of slope information is very detrimental. Second, standard ML losses do not work well in combinatorial settings. A growing body of research addresses these challenges through diverse methods. Unfortunately, the lack of well-maintained implementations slows down the adoption of CO layers. In this paper, building upon previous works, we introduce a probabilistic perspective on CO layers, which lends itself naturally to approximate differentiation and the construction of structured losses. We recover many approaches from the literature as special cases, and we also derive new ones. Based on this unifying perspective, we present InferOpt.jl, an open-source Julia package that 1) allows turning any CO oracle with a linear objective into a differentiable layer, and 2) defines adequate losses to train pipelines containing such layers. Our library works with arbitrary optimization algorithms, and it is fully compatible with Julia's ML ecosystem. We demonstrate its abilities using a pathfinding problem on video game maps as guiding example, as well as three other applications from operations research.

Published
2022

65. Comparing Parallel Surrogate-based and Surrogate-free Multi-Objective Optimization of COVID-19 vaccines allocation

Author

Briffoteaux, Guillaume, Ragonnet, Romain, Tomenko, Pierre, Mezmaz, Mohand, Melab, Nouredine, Tuyttens, Daniel, University of Mons [Belgium] (UMONS), Optimisation de grande taille et calcul large échelle (BONUS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Monash University [Melbourne], and Briffoteaux, Guillaume

Subjects
[INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; The simulation-based and computationally expensive problem tackled in this paper addresses COVID-19 vaccines allocation in Malaysia. The multi-objective formulation considers simultaneously the total number of deaths, peak hospital occupancy and relaxation of mobility restrictions. Evolutionary algorithms have proven their capability to handle multi-to-many objectives but require a high number of computationally expensive simulations. The available techniques to raise the challenge rely on the joint use of surrogate-assisted optimization and parallel computing to deal with computational expensiveness. On the one hand, the simulation software is imitated by a cheap-to-evaluate surrogate model. On the other hand, multiple candidates are simultaneously assessed via multiple processing cores. In this study, we compare the performance of recently proposed surrogate-free and surrogate-based parallel multi-objective algorithms through the application to the COVID-19 vaccine distribution problem.

Published
2022

66. Efficient Low Rank Convex Bounds for Pairwise Discrete Graphical Models

Author

Durante, Valentin, Katsirelos, George, Schiex, Thomas, Schiex, Thomas, and Artificial and Natural Intelligence Toulouse Institute - - ANITI2019 - ANR-19-P3IA-0004 - P3IA - VALID

Subjects
[INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Convex Optimization, Low rank, Graphical Models, Discrete Optimization, Semi-Definite Programming, Maximum A Posteriori
Abstract

In this paper, we extend a Burer-Monteiro style method to compute low rank Semi-Definite Programming (SDP) bounds for the MAP problem on discrete graphical models with an arbitrary number of states and arbitrary pairwise potentials. We consider both a penalized constraint approach and a dedicated Block Coordinate Descent (BCD) approach which avoids large penalty coefficients in the cost matrix. We show our algorithm is decreasing. Experiments show that the BCD approach compares favorably to the penalized approach and to usual linear bounds relying on convergent message passing approaches., Dans ce travail, nous étendons une méthode de type Burer-Monteiro pour calculer des minorants convexes (relaxation demi-définie positive) pour le problème de Maximum d'a Posteriori dans des modèles graphiques discrets où les variables ont un nombre d'états et des potentiels binaires arbitraires. Nous considérons une méthode incluant une contrainte pénalisée et une algorithme de type descente en coordonnées par bloc qui évite l’apparition de coefficient de magnitude importante dans la matrice de coûts. Nous montrons que l'algorithme est décroissant. Une évaluation empirique montre que l'approche BCD se compare favorablement à l'approche pénalisée et des minorants linéaires usuels, tels que ceux basés sur des approches de type "message passing" convergentes.

Published
2022
Full Text
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67. Remarks on the controllability of parabolic systems with non-diagonalizable diffusion matrix

Author

Duprez, Michel, González-Burgos, Manuel, Souza, Diego A., Computational Anatomy and Simulation for Medicine (MIMESIS), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie (ICube), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), IMUS, Departamento de Ecuaciones Differenciales y Analysis numérico [Sevilla] (EDAN), Facultad de Matemáticas, ANR-20-CE40-0009,TRECOS,Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux(2020), Duprez, Michel, Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux - - TRECOS2020 - ANR-20-CE40-0009 - AAPG2020 - VALID, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie (ICube), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), and Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Optimization and Control (math.OC), 93B05, 93C20, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Optimization and Control
Abstract

International audience; The distributed null controllability for coupled parabolic systems with non-diagonalizable diffusion matrices with a reduced number of controls has been studied in the case of constant matrices. On the other hand, boundary controllability issues and distributed controllability with non-constant coefficients for this kind of systems is not completely understood. In this paper, we analyze the boundary controllability properties of a class of coupled parabolic systems with nondiagonalizable diffusion matrices in the constant case and the distributed controllability of a 2 × 2 non-diagonalizable parabolic system with space-dependent coefficients. For the boundary controllability problem, our strategy relies on the moment method. For the distributed controllability problem, our findings provide positive and negative control results by using the Fattorini-Hautus test and a fictitious control strategy.

Published
2022

68. Benchmarking an algorithm for expensive high-dimensional objectives on the bbob and bbob-largescale testbeds

Author

Hoffman, Zachary, Huntsman, Steve, and Huntsman, Steve

Subjects
[INFO.INFO-NE] Computer Science [cs]/Neural and Evolutionary Computing [cs.NE], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]
Abstract

We report benchmarks for a recently developed algorithm on the bbob and bbob-largescale benchmarking testbeds in COCO. This algorithm is designed for expensive high-dimensional multimodal objectives (such as arise in hyperparameter optimization or via simulations), and this regime introduces challenges for benchmarking. In particular, while the COCO experimental procedure yields evidence that this algorithm improves on the state of the art, the COCO framework also exhibits shortcomings for the very low evaluation budgets involved here. Consequently, we also report the results of ad hoc experiments that demonstrate a more obvious if less rigorous advantage for the algorithm over its nearest competition.

Published
2022

69. Subsampling under distributional constraints

Author

Combes, Florian, Fraiman, Ricardo, Ghattas, Badih, COMBES, Florian, Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Centro de Matematica [Uruguay] (CMAT), and Universidad de la República [Montevideo] (UDELAR)

Subjects
numerical models, Kolmogorov–Smirnov, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Optimal sampling, nearest neighbours, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Abstract

Some complex models are frequently employed to describe physical and mechanical phenomena. In this setting we have an input X in a general space, and an output Y = f(X) where f is a very complicated function, whose computational cost for every new input is very high. We are given two sets of observations of X, S1 and S2 of different sizes such that only f(S1) is available. We tackle the problem of selecting a subset S3 ⊂ S2 of smaller size on which to run the complex mode f, and such that the empirical distribution of f(S3) is close to that of f(S1). We suggest three algorithms to solve this problem and show their efficiency using simulated datasets and the Airfoil self-noise data set.

Published
2022

70. ADMM-Based Residual Whiteness Principle for Automatic Parameter Selection in Single Image Super-Resolution Problems

Author

Monica Pragliola, Luca Calatroni, Alessandro Lanza, Fiorella Sgallari, Department of Mathematics [Bologna], Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Calatroni, Luca, Pragliola, Monica, Lanza, Alessandro, Sgallari, Fiorella, Pragliola, M, Calatroni, L, Lanza, A, and Sgallari, F

Subjects
Statistics and Probability, Applied Mathematics, Single image super-resolution, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Condensed Matter Physics, Residual whiteness principle, Sparse regularisation, [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], Modeling and Simulation, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Geometry and Topology, Computer Vision and Pattern Recognition, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], ADMM, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Total variation regularisation
Abstract

We propose an automatic parameter selection strategy for the single image super-resolution problem for images corrupted by blur and additive white Gaussian noise with unknown standard deviation. The proposed approach exploits the structure of both the down-sampling and the blur operators in the frequency domain and computes the optimal regularisation parameter as the one optimising a suitably defined residual whiteness measure. Computationally, the proposed strategy relies on the fast solution of generalised Tikhonov $$\ell _2$$ ℓ 2 –$$\ell _2$$ ℓ 2 problems as proposed in Zhao et al. (IEEE Trans Image Process 25:3683–3697, 2016). These problems naturally appear as substeps of the Alternating Direction Method of Multipliers used to solve single image super-resolution problems with non-quadratic, non-smooth, sparsity-promoting regularisers both in convex and in non-convex regimes. After detailing the theoretical properties allowing to express the whiteness functional in a compact way, we report an exhaustive list of numerical experiments proving the effectiveness of the proposed approach for different type of problems, in comparison with well-known parameter selection strategies such as, e.g., the discrepancy principle.

Published
2022

71. Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients

Author

Magron, Victor, Din, Mohab Safey El, Schweighofer, Markus, Vu, Trung Hieu, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Sorbonne Université (SU), Polynomial Systems (PolSys), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Fachbereich Mathematik und Statistik, University of Konstanz, ANR-18-ERC2-0004,COPS,Optimisation garantie pour la vérification des systèmes cyber-physiques(2018), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Magron, Victor, TREMPLIN-ERC - Optimisation garantie pour la vérification des systèmes cyber-physiques - - COPS2018 - ANR-18-ERC2-0004 - TERC - VALID, Artificial and Natural Intelligence Toulouse Institute - - ANITI2019 - ANR-19-P3IA-0004 - P3IA - VALID, Centre International de Mathématiques et d'Informatique (de Toulouse) - - CIMI2011 - ANR-11-LABX-0040 - LABX - VALID, and Polynomial Optimization, Efficiency through Moments and Algebra - POEMA - - H20202019-01-01 - 2022-12-31 - 813211 - VALID

Subjects
FOS: Computer and information sciences, Computer Science - Symbolic Computation, Optimization and Control (math.OC), ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, FOS: Mathematics, MathematicsofComputing_NUMERICALANALYSIS, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Symbolic Computation (cs.SC), Mathematics - Optimization and Control
Abstract

Certifying the positivity of trigonometric polynomials is of first importance for design problems in discrete-time signal processing. It is well known from the Riesz-Fej\'ez spectral factorization theorem that any trigonometric univariate polynomial positive on the unit circle can be decomposed as a Hermitian square with complex coefficients. Here we focus on the case of polynomials with Gaussian integer coefficients, i.e., with real and imaginary parts being integers. We design, analyze and compare, theoretically and practically,three hybrid numeric-symbolic algorithms computing weighted sums of Hermitian squares decompositions for trigonometric univariate polynomials positive on the unit circle with Gaussian coefficients. The numerical steps the first and second algorithm rely on are complex root isolation and semidefinite programming, respectively. An exact sum of Hermitian squares decomposition is obtained thanks to compensation techniques. The third algorithm, also based on complex semidefinite programming, is an adaptation of the rounding and projection algorithm by Peyrl and Parrilo. For all three algorithms, we prove bit complexity and output size estimates that are polynomial in the degree of the input and linear in the maximum bitsize of its coefficients. We compare their performance on randomly chosen benchmarks, and further design a certified finite impulse filter., Comment: 8 pages, 1 table

Published
2022

72. Non-smooth Bayesian learning for artificial neural networks

Author

Mohamed Fakhfakh, Lotfi Chaari, Bassem Bouaziz, Faiez Gargouri, and Chaari, Lotfi

Subjects
Machine Learning, Optimization, [INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], Bayesian methods, General Computer Science, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Artificial Neural Networks, Hamiltonian dynamics, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
Abstract

Artificial Neural Networks (ANNs) are being widely used in supervised Machine Learning (ML) to analyze signals or images for many applications. Using an annotated learning database, one of the main challenges is to optimize the network weights. A lot of work on solving optimization problems or improving optimization methods in machine learning has been proposed successively such as gradient-based method, Newton-type method, meta-heuristic method. Moreover, sparse regularizer is designed to zero superfluous weights and hence remove unneeded connections. However, if one wants to promote sparse networks, such as the 1 norm, one need use sparse regularizations, the optimization process becomes challenging since the error to be minimized is no longer differentiable. In this paper, we propose an MCMC-based optimization scheme formulated in a Bayesian framework. The proposed scheme solves the above-mentioned sparse optimization problem using an efficient sampling scheme and Hamiltonian dynamics. The designed optimizer is conducted on four datasets, two COVID-19 and two standard datasets (Fashion-MNIST and CIFAR-10). The results are verified by a comparative study with three different CNNs, one of which is deeper than the others in order to evaluate the effectiveness of our optimizer. Promising results show the usefulness of the proposed method to allow ANNs, even with low complexity levels, reaching high accuracy rates of up to 94% in most of the experiments carried out. The proposed method is also faster and more robust concerning overfitting issues. More importantly, the training step of the proposed method is much faster than all competing algorithms.

Published
2022

73. GTL-VILLE: Experimental platform for urban traffic state estimation

Author

Rodriguez-Vega, Martin, Senique, Leo, Canudas de Wit, Carlos, Dynamics and Control of Networks (DANCE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-GIPSA Pôle Automatique et Diagnostic (GIPSA-PAD), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Grenoble Alpes (UGA), European Project: 694209,Advanced Grant (AdG), ERC-2015-AdG ,Scale-FreeBack(2016), Rodriguez-Vega, Martin, and Scale-Free Control for Complex Physical Network Systems - Scale-FreeBack - - Advanced Grant (AdG), ERC-2015-AdG 2016-09-01 - 2021-08-31 - 694209 - VALID

Subjects
Emission/consumption estimation, [SPI.GCIV.IT]Engineering Sciences [physics]/Civil Engineering/Infrastructures de transport, Traffic data, [SPI.GCIV.IT] Engineering Sciences [physics]/Civil Engineering/Infrastructures de transport, Vehicle density prediction, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Grenoble downtown
Abstract

National audience; The GTL-Ville is an online experimental platform for the real-time collection and visualization of traffic data for the city of Grenoble in France. The platform processes real-time traffic data to calculate macroscopic traffic indicators such as flow, density, speed, traveling time and vehicle emissions. The platform was developed by the ERC project Scale-FreeBack, to showcase the various innovative methods and techniques developed by the team, such as sensor location, density reconstruction and prediction, and travel time estimation.

Published
2022

74. Coupling Architecture Framework and Operation Research: the Case of NAF with Cost and Delay Driven Multi-Criteria Scheduling

Author

Brisacier-Porchon, Lorraine, Hammami, Omar, and BRISACIER-PORCHON, Lorraine

Subjects
Optimization, Operation Research, [SPI.OTHER] Engineering Sciences [physics]/Other, Architecture, NAF v3.1, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC]
Abstract

Architecture frameworks are essential tools to model system of systems. The aim of the NATO Architecture Framework (NAF) is to provide a standard for developing and describing architectures for both military and business use. A main purpose is to contribute to the analysis and development of alternative architectures, evaluate and compare them. In this regard AF itself is not sufficient to evaluate alternative architectures and evaluation tools are needed ideally in a seamless way. In this paper we propose a coupling between NAF and operations research, NAF-OR, through linear programming in order to assess the various possible scheduling and resource derived from the different architectures. This in turn improves system design productivity. While management techniques in system engineering and program modifications are based on best effort to respect schedule and budget, this article introduces the benefits of using optimization to input validated data NAF through a significant example using multi-objective scheduling problem introducing NAF-OR, a method that combines NAF and Operation research.

Published
2022

75. Weighting Schemes for One-Shot Federated Learning

Author

Garin, Marie, Evgeniou, Theodoros, Vayatis, Nicolas, CB - Centre Borelli - UMR 9010 (CB), Service de Santé des Armées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)-Université Paris Cité (UPCité), Institut Européen d'administration des Affaires (INSEAD), and Garin, Marie

Subjects
Optimization, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], MSE, ERM, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Privacy, [INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Distributed Learning, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Federated Learning, Ensemble Learning
Abstract

This paper focuses on one-shot aggregation of statistical estimations made across disjoint data sources for federated learning, in the context of empirical risk minimization. We exploit the role of each local sample size for this problem to develop a new weighting scheme for one-shot federated learning. First, we provide upper bounds on the local errors and biases from which we derive an upper bound for the plain federated learning parameter. Then, by casting an optimization problem based on the bias-variance decomposition of the MSE, we develop a simple weighting scheme based only on the local sample sizes. The proposed procedure can be embedded in a wide variety of algorithms used for federated learning. Finally, we evaluate our procedure in the context of large-scale estimation of linear models with ridge regression and compare it to the typical choice of weights in federated learning. We observe that, due to unbalanced sample sizes across the data sources, the proposed weighting scheme outperforms the standard one and converges faster to the performance of a centralized estimator.

Published
2022

76. Stability of Linear Systems under Extended Weakly-Hard Constraints

Author

Victor Magron, Nils Vreman, Jie Wang, Paolo Pazzaglia, Martina Maggio, Automatic Control Group [Lund], Lund University [Lund], Saarland University [Saarbrücken], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Equipe Polynomial OPtimization (LAAS-POP), ANR-18-ERC2-0004,COPS,Optimisation garantie pour la vérification des systèmes cyber-physiques(2018), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Magron, Victor, TREMPLIN-ERC - Optimisation garantie pour la vérification des systèmes cyber-physiques - - COPS2018 - ANR-18-ERC2-0004 - TERC - VALID, Artificial and Natural Intelligence Toulouse Institute - - ANITI2019 - ANR-19-P3IA-0004 - P3IA - VALID, and Polynomial Optimization, Efficiency through Moments and Algebra - POEMA - - H20202019-01-01 - 2022-12-31 - 813211 - VALID

Subjects
Control and Optimization, Optimization and Control (math.OC), Control and Systems Engineering, FOS: Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control
Abstract

Control systems can show robustness to many events, like disturbances and model inaccuracies. It is natural to speculate that they are also robust to sporadic deadline misses when implemented as digital tasks on an embedded platform. This paper proposes a comprehensive stability analysis for control systems subject to deadline misses, leveraging a new formulation to describe the patterns experienced by the control task under different handling strategies. Such analysis brings the assessment of control systems robustness to computational problems one step closer to the controller implementation., 6 pages, 1 table, published in IEEE Control Systems Letters and in the proceedings of the Control and Decision Conference 2022

Published
2022

77. $\Gamma$-convergence for a class of action functionals induced by gradients of convex functions

Author

Yann Brenier, Luigi Ambrosio, Aymeric Baradat, Scuola Normale Superiore di Pisa (SNS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Département de Mathématiques et Applications - ENS Paris (DMA), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Baradat, Aymeric, Ambrosio, L., Baradat, A., Brenier, Y., Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Pure mathematics, General Mathematics, Hilbert space, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], stability, Strong topology (polar topology), Mosco convergence, symbols.namesake, action functional, L-convexity, Γ-convergence, Real-valued function, Settore MAT/05 - Analisi Matematica, symbols, Large deviations theory, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Nabla symbol, Convex function, Mathematics - Optimization and Control, Rate function, Mathematics
Abstract

Given a real function $f$, the rate function for the large deviations of the diffusion process of drift $\nabla f$ given by the Freidlin-Wentzell theorem coincides with the time integral of the energy dissipation for the gradient flow associated with $f$. This paper is concerned with the stability in the hilbertian framework of this common action functional when $f$ varies. More precisely, we show that if $(f_h)_h$ is uniformly $\lambda$-convex for some $\lambda \in \mathbb{R}$ and converges towards $f$ in the sense of Mosco convergence, then the related functionals $\Gamma$-converge in the strong topology of curves.

Published
2021

78. On a Phase Transition of Regret in Linear Quadratic Control: The Memoryless Case

Author

Ingvar Ziemann, Henrik Sandberg, Ziemann, Ingvar, and Royal Institute of Technology [Stockholm] (KTH )

Subjects
0209 industrial biotechnology, Control and Optimization, Adaptive control, Rank (linear algebra), Logarithm, MIMO, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Regret, 02 engineering and technology, 01 natural sciences, Linear subspace, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], 010104 statistics & probability, symbols.namesake, 020901 industrial engineering & automation, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Square root, Control and Systems Engineering, symbols, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Fisher information, Mathematics
Abstract

We consider an idealized version of adaptive control of a MIMO system without state. We demonstrate how rank deficient Fisher information in this simple memoryless problem leads to the impossibility of logarithmic rates of regret. This to some extent resolves an open issue concerning the attainability of logarithmic regret rates in linear quadratic adaptive control. Our analysis rests on a version of the Cramér-Rao inequality that takes into account possible ill-conditioning of Fisher information and a pertubation result on the corresponding singular subspaces. This is used to define a sufficient condition, which we term uniformativeness, for regret to be at least order square root in the samples.

Published
2021

79. Fluorescence image deconvolution microscopy via generative adversarial learning (FluoGAN)

Author

Mayeul Cachia, Vasiliki Stergiopoulou, Luca Calatroni, Sebastien Schaub, Laure Blanc-Féraud, Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Institut de la Mer de Villefranche (IMEV), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Supported by EMBRC-France, whose French state funds are managed by the ANR within the Investments of the Future program under reference ANR-10-INBS-0. The work of VS and LBF has been supported by the French government, through the 3IA Cˆote d’Azur Investments in the Future project managed by the National Research Agency, grant ANR-19-P3IA-0002. VS, LBF and LC acknowledge the support by the ANR MICROBLIND grant ANR-21-CE48-0008., ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019), ANR-21-CE48-0008,MICROBLIND,Problèmes inverses aveugles et microscopie optique(2021), European Project: 777826,NoMADS(2018), Stergiopoulou, Vasiliki, 3IA Côte d'Azur - - 3IA@cote d'azur2019 - ANR-19-P3IA-0002 - P3IA - VALID, Problèmes inverses aveugles et microscopie optique - - MICROBLIND2021 - ANR-21-CE48-0008 - AAPG2021 - VALID, Nonlocal Methods for Arbitrary Data Sources - NoMADS - 2018-03-01 - 2022-02-28 - 777826 - VALID, and Supported by EMBRC-France, whose French state funds are managed by the ANR within the Investments of the Future program under reference ANR-10-INBS-0. The work of VS and LBF has been supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency, grant ANR-19-P3IA-0002. VS, LBF and LC acknowledge the support by the ANR MICROBLIND grant ANR-21-CE48-0008. LC acknowledges the support received by the GdR ISIS grant SPLIN and by the IEA CNRS grant VaMOS.

Subjects
[PHYS.PHYS.PHYS-OPTICS] Physics [physics]/Physics [physics]/Optics [physics.optics], [PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics], Applied Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Computer Science Applications, Theoretical Computer Science, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Signal Processing, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematical Physics
Abstract

We propose FluoGAN, an unsupervised hybrid approach combining the physical modelling of fluorescence microscopy timelapse acquisitions with a generative adversarial learning procedure for the problem of image deconvolution. Differently from standard approaches combining a least-square data term based on one (long-time exposure) image with sparsity-promoting regularisation terms, FluoGAN relies on a data term being the distributional distance between the fluctuating observed timelapse (short-time exposure images) and the generative model. Such distance is computed by adversarial training of two competing architectures: a physics-inspired generator simulating the fluctuating behaviour as a Poisson process of the observed images combined with blur and undersampling, and a standard convolutional discriminator network. FluoGAN is a fully unsupervised approach requiring only a fluctuating sequence of blurred, undersampled and noisy images of the sample of interest as input. It can be complemented with prior knowledge on the desired solution such as sparsity, non-negativity etc. After having described the main ideas behind FluoGAN, we formulate the corresponding optimisation problem and report several results on simulated and real phantoms used by microscopy engineers to quantitatively assess spatial resolution. The comparison of FluoGAN with state-of-the-art methodologies shows improved resolution, allowing for high-precision reconstructions of fine structures in challenging real Ostreopsis cf Ovata data. The FluoGAN code is available at: https://github.com/cmayeul/FluoGAN.

Published
2023

80. Robust optimal control of stochastic hyperelastic materials

Author

Jesús Martínez-Frutos, Francisco Periago, Rogelio Ortigosa, Pablo Pedregal, and Ortigosa, Rogelio

Subjects
soft robotics, Computer science, [MATH] Mathematics [math], 02 engineering and technology, Expected value, 01 natural sciences, 0203 mechanical engineering, Robustness (computer science), 0103 physical sciences, Applied mathematics, hyperelasticity, Robust optimal control, 010301 acoustics, Applied Mathematics, turgor pressure, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Optimal control, Controllability, Nonlinear system, 020303 mechanical engineering & transports, material uncertainty, Modeling and Simulation, Hyperelastic material, Robot, Minification, active fibers
Abstract

Soft robots are highly nonlinear systems made of deformable materials such as elastomers, fluids and other soft matter, that often exhibit intrinsic uncertainty in their elastic responses under large strains due to microstructural inhomogeneity. These sources of uncertainty might cause a change in the dynamics of the system leading to a significant degree of complexity in its controllability. This issue poses theoretical and numerical challenges in the emerging field of optimal control of stochastic hyperelasticity. This paper states and solves the robust averaged control in stochastic hyperelasticity where the underlying state system corresponds to the minimization of a stochastic polyconvex strain energy function. Two bio-inspired optimal control problems under material uncertainty are addressed. The expected value of the L2-norm to a given target configuration is minimized to reduce the sensitivity of the spatial configuration to variations in the material parameters. The existence of optimal solutions for the robust averaged control problem is proved. Then the problem is solved numerically by using a gradient-based method. Two numerical experiments illustrate both the performance of the proposed method to ensure the robustness of the system and the significant differences that may occur when uncertainty is incorporated in this type of control problems.

Published
2020

81. Automatic differentiation of nonsmooth iterative algorithms

Author

Bolte, Jérôme, Pauwels, Edouard, Vaiter, Samuel, Pauwels, Edouard, Artificial and Natural Intelligence Toulouse Institute - - ANITI2019 - ANR-19-P3IA-0004 - P3IA - VALID, Mathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond - - MaSDOL2019 - ANR-19-CE23-0017 - AAPG2019 - VALID, and APPEL À PROJETS GÉNÉRIQUE 2018 - Méthodes variationnelles pour les signaux sur graphe - - GraVa2018 - ANR-18-CE40-0005 - AAPG2018 - VALID

Subjects
FOS: Computer and information sciences, [INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], Computer Science - Machine Learning, Optimization and Control (math.OC), FOS: Mathematics, Mathematics::Optimization and Control, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Mathematics - Optimization and Control, Computer Science::Databases, Machine Learning (cs.LG)
Abstract

Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is well understood for many smooth problems but the nondifferentiable case is hardly considered. Is there a limiting object for nonsmooth piggyback automatic differentiation (AD)? Does it have any variational meaning and can it be used effectively in machine learning? Is there a connection with classical derivative? All these questions are addressed under appropriate nonexpansivity conditions in the framework of conservative derivatives which has proved useful in understanding nonsmooth AD. For nonsmooth piggyback iterations, we characterize the attractor set of nonsmooth piggyback iterations as a set-valued fixed point which remains in the conservative framework. This has various consequences and in particular almost everywhere convergence of classical derivatives. Our results are illustrated on parametric convex optimization problems with forward-backward, Douglas-Rachford and Alternating Direction of Multiplier algorithms as well as the Heavy-Ball method.

Published
2022

82. Splitting games over finite sets

Author

Frédéric Koessler, Marie Laclau, Jérôme Renault, Tristan Tomala, Paris School of Economics (PSE), École des Ponts ParisTech (ENPC)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Centre National de la Recherche Scientifique (CNRS), Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH), Ecole des Hautes Etudes Commerciales (HEC Paris)-Centre National de la Recherche Scientifique (CNRS), Ecole des Hautes Etudes Commerciales (HEC Paris), Toulouse School of Economics (TSE), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Université Fédérale Toulouse Midi-Pyrénées, ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), ANR-15-CE38-0007,CIGNE,Communication et Information dans des Jeux dans des Réseaux(2015), ANR-19-CE26-0010,StratCom,Diffusion de l'information en présence de rationalité limitée et de canaux de transmission complexes(2019), ANR-19-CE23-0017,MaSDOL,Mathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond(2019), Renault, Jérôme, Artificial and Natural Intelligence Toulouse Institute - - ANITI2019 - ANR-19-P3IA-0004 - P3IA - VALID, DS0806 - Révolution numérique et mutations sociales - Communication et Information dans des Jeux dans des Réseaux - - CIGNE2015 - ANR-15-CE38-0007 - AAPG2015 - VALID, Diffusion de l'information en présence de rationalité limitée et de canaux de transmission complexes - - StratCom2019 - ANR-19-CE26-0010 - AAPG2019 - VALID, and Mathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond - - MaSDOL2019 - ANR-19-CE23-0017 - AAPG2019 - VALID

Subjects
Splitting games, Bayesian games, Information design, General Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Repeated games with incomplete information, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Bayesian persuasion, MSC :91A1591A27, Mertens-Zamir system, B- ECONOMIE ET FINANCE, Software
Abstract

This paper studies zero-sum splitting games with finite sets of states. Players dynamically choose a pair of martingales {pt,qt}t, in order to control a terminal payoff u(p∞,q∞). A first part introduces the notion of “Mertens–Zamir transform" of a real-valued matrix and use it to approximate the solution of the Mertens–Zamir system for continuous functions on the square [0,1]2. A second part considers the general case of finite splitting games with arbitrary correspondences containing the Dirac mass on the current state: building on Laraki and Renault (Math Oper Res 45:1237–1257, 2020), we show that the value exists by constructing non Markovian ε-optimal strategies and we characterize it as the unique concave-convex function satisfying two new conditions.

Published
2022

83. Off-the-grid curve reconstruction through divergence regularisation: an extreme point result

Author

Laville, Bastien, Blanc-Féraud, Laure, Aubert, Gilles, Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-17-EURE-0004,UCA DS4H,UCA Systèmes Numériques pour l'Homme(2017), ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Signal, Images et Systèmes (Laboratoire I3S - SIS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laville, Bastien, UCA Systèmes Numériques pour l'Homme - - UCA DS4H2017 - ANR-17-EURE-0004 - EURE - VALID, and 3IA Côte d'Azur - - 3IA@cote d'azur2019 - ANR-19-P3IA-0002 - P3IA - VALID

Subjects
divergence vector field, Off-the-grid inverse problem, curve reconstruction, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], imaging, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Radon measures, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], extreme points, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Abstract

We propose a new strategy for the reconstruction of curves in an image through an off-the-grid variational framework, inspired by the reconstruction of spikes in the literature. We introduce a new functional CROC on the space of 2-dimensional Radon measures with finite divergence denoted , and we establish several theoretical tools through the definition of a certificate. Our main contribution lies in the sharp characterisation of the extreme points of the unit ball of the-norm: there are exactly measures supported on 1-rectifiable oriented simple Lipschitz curves, thus enabling a precise characterisation of our functional minimisers and further opening a promising avenue for the algorithmic implementation.

Published
2022

84. Synthesis of Input-to-State Safety and Attractivity Controllers using Nested Sequences of Abstractions

Author

Apaza-Perez, W. A., Girard, Antoine, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), European Project: 725144,H2020 Pilier ERC,PROCSYS(2017), Girard, Antoine, and Towards programmable cyber-physical systems: a symbolic control approach - PROCSYS - - H2020 Pilier ERC2017-09-01 - 2022-08-31 - 725144 - VALID

Subjects
[INFO.INFO-SY] Computer Science [cs]/Systems and Control [cs.SY], [SPI.AUTO] Engineering Sciences [physics]/Automatic, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

In this paper, we introduce a notion of input-to-statesafety (ISSf) and input-to-state attractivity (ISA) controllers for fi-nite state dynamical systems. Using such controllers, the deviationof the closed-loop trajectories from a safe or from a target setcan be bounded by a gain function that is increasing with respectto the amplitude of the disturbances. We show the existence ofcontrollers that are least violating (LV) in the sense that their gainfunction is minimal (with respect to a certain order on the set ofgain functions) over all possible ISSf and ISA controllers. Then,we consider the problem of synthesizing these LV-ISSf and LV-ISAcontrollers for the colexicographic order on gain functions. Wepresent an approach that is based on successive refinements ofcontrollers: starting from a controller synthesized against worst-case disturbances, the controller is iteratively refined in order toimprove the closed-loop behavior under disturbances of lower am-plitude. We prove that our method makes it possible to synthesizea LV-ISSf controller, and an ISA controller that is shown to be aLV-ISA controller when an easily checkable condition is satisfied.We discuss how these results can be used to synthesize robustcontrollers for nonlinear continuous-time systems via symboliccontrol techniques. Finally, we show an application to adaptivecruise control to demonstrate the effectiveness of our approach

Published
2022

85. Internal layer intersecting the boundary of a domain in a singular advection-diffusion equation

Author

Amirat, Youcef, Munch, Arnaud, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and Munch, Arnaud

Subjects
Asymptotic analysis, Sobolev estimates AMS subject classification (2020): 35C20, 35K67, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Internal and boundary layers, Singular perturbation
Abstract

We perform an asymptotic analysis with respect to the parameter ε > 0 of the solution of the scalar advection-diffusion equation y ε t +M (x, t)y ε x −εy ε xx = 0, (x, t) ∈ (0, 1)×(0, T), supplemented with Dirichlet boundary conditions. For small values of ε, the solution y ε exhibits a boundary layer of size O(ε) in the neighborhood of x = 1 (assuming M > 0) and an internal layer of size O(ε 1/2) in the neighborhood of the characteristic starting from the point (0, 0). Assuming that these layers interact each other after a finite time T > 0 and using the method of matched asymptotic expansions, we construct an explicit approximation P ε satisfying y ε − P ε L ∞ (0,T ;L 2 (0,1)) = O(ε 1/2). We emphasize the additional difficulties with respect to the case M constant considered recently by the authors.

Published
2022

86. Equivalent formulations of the minmum peak problem and applications

Author

Molina, Emilio, Rapaport, Alain, Ramirez Cabrera, Hector, Center for Mathematical Modeling (CMM), Universidad de Chile = University of Chile [Santiago] (UCHILE), Departamento de Ingeniería Matemática [Santiago] (DIM), Universidad de Chile = University of Chile [Santiago] (UCHILE)-Centre National de la Recherche Scientifique (CNRS), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut Agro Montpellier, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), ANID-PFCHA/Doctorado Nacional/2018-21180348 (Chile), FONDECYT grant 1201982 (Chile), ACE210010 and FB210005, BASAL funds for center of excellence, ANID Chile, and Rapaport, Alain

Subjects
[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience

Published
2022

87. Searching for an MR Fingerprinting sequence to measure brain oxygenation without contrast agent

Author

Coudert, Thomas, Delphin, Aurelien, Warnking, Jan, Lemasson, Benjamin, Barbier, Emmanuel L, Christen, Thomas, [GIN] Grenoble Institut des Neurosciences (GIN), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Grenoble Alpes (UGA), MoGimaging Network, HTE Program of the French Cancer Plan, Toulouse, France, and Coudert, Thomas

Subjects
[SDV.BIO]Life Sciences [q-bio]/Biotechnology, [PHYS.PHYS.PHYS-MED-PH] Physics [physics]/Physics [physics]/Medical Physics [physics.med-ph], [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, [SCCO.NEUR]Cognitive science/Neuroscience, [SCCO.NEUR] Cognitive science/Neuroscience, [SCCO.COMP]Cognitive science/Computer science, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [SDV.BC]Life Sciences [q-bio]/Cellular Biology, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], [SDV.BIO] Life Sciences [q-bio]/Biotechnology, [SDV.IB.IMA] Life Sciences [q-bio]/Bioengineering/Imaging, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], [SCCO.COMP] Cognitive science/Computer science, [PHYS.PHYS.PHYS-MED-PH]Physics [physics]/Physics [physics]/Medical Physics [physics.med-ph], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [SDV.BC] Life Sciences [q-bio]/Cellular Biology
Abstract

International audience; We propose to use numerical simulations and Monte Carlo approaches to test 40 MR fingerprinting sequences for their ability to quantify the BOLD effect and provide maps of baseline blood oxygen saturation without the need for contrast agent injection. Our results suggest that several sequences can produce SO2 maps with less that 3% error on average even in the presence of B1 and B0 inhomogeneities. T2 and blood vessel radius could also be estimated with the same acquisitions.

Published
2022

88. Optimizing the beam selection for non-coplanar VMAT by using simulated annealing approach

Author

Salih Abdelaziz, Nicolas Boussion, Julien Bert, Franklin Okoli, Dimitris Visvikis, Laboratoire de Traitement de l'Information Medicale (LaTIM), Université de Brest (UBO)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre Hospitalier Régional Universitaire de Brest (CHRU Brest)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Institut Brestois Santé Agro Matière (IBSAM), Université de Brest (UBO), Robotique médicale et mécanismes parallèles (DEXTER), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Abdelaziz, Salih, Institut National de la Santé et de la Recherche Médicale (INSERM)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Centre Hospitalier Régional Universitaire de Brest (CHRU Brest)-Université de Brest (UBO)-Institut Brestois Santé Agro Matière (IBSAM), and Conception et commande de robots pour la manipulation (DEXTER)

Subjects
Beam selection, Computer science, [PHYS.NEXP] Physics [physics]/Nuclear Experiment [nucl-ex], Context (language use), treatment planning optimization, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Trajectory optimization, Degrees of freedom (mechanics), [PHYS.NEXP]Physics [physics]/Nuclear Experiment [nucl-ex], Atomic and Molecular Physics, and Optics, 3. Good health, Simulated annealing, noncoplanar volumetric modulated arc therapy (VMAT), simulated annealing (SA), Benchmark (computing), Radiology, Nuclear Medicine and imaging, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Greedy algorithm, Instrumentation, Algorithm, Beam (structure), Selection (genetic algorithm), radiotherapy
Abstract

International audience; Non-coplanar VMAT treatment can achieve better organ-at-risk (OAR) avoidance by orienting the radiation beams in a different geometric plane relative to the patient. However, determining the optimal set of beam orientations is challenging due to the additional degrees of freedom. The objective of this study was to use Simulated Annealing (SA) for beam selection in noncoplanar VMAT optimization context. SA method was combined with a direct leaf trajectory optimization approach to obtain a set of globally optimal beams which serve as control points for the treatment trajectory. Proposed method was evaluated through the TG119 benchmark and two clinical cases (prostate and liver cancers). Finally, the SA beam selection method was compared to the standard coplanar and non-coplanar beam selection approach. The results showed an accurate delivery of the prescription dose to the target tumor volume in all cases. Generally, not on every organ, the non-coplanar SA method showed better organ-at-risk (OAR) sparing compared to the coplanar and non-coplanar greedy method. This work demonstrates that optimized non-coplanar beam orientations using the proposed SA method can be more clinically interesting than coplanar method in some specific patient cases.

Published
2022

89. Exact controllability to eigensolutions for evolution equations of parabolic type via bilinear control

Author

Fatiha Alabau-Boussouira, Piermarco Cannarsa, Cristina Urbani, and Alabau-Boussouira, Fatiha

Subjects
Applied Mathematics, Evolution equations, Exact controllability, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Bilinear control, Parabolic PDEs, [MATH] Mathematics [math], 35Q93, 93C25, 93C10, 93B05, 35K90, Mathematics - Analysis of PDEs, Optimization and Control (math.OC), FOS: Mathematics, Control cost, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Optimization and Control, Analysis, Analysis of PDEs (math.AP)
Abstract

In a separable Hilbert space $X$, we study the controlled evolution equation \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0, \end{equation*} where $A\geq-\sigma I$ ($\sigma\geq0$) is a self-adjoint linear operator, $B$ is a bounded linear operator on $X$, and $p\in L^2_{loc}(0,+\infty)$ is a bilinear control. We give sufficient conditions in order for the above nonlinear control system to be locally controllable to the $j$th eigensolution for any $j\geq1$. We also derive semi-global controllability results in large time and discuss applications to parabolic equations in low space dimension. Our method is constructive and all the constants involved in the main results can be explicitly computed., Comment: 29 pages, 2 figures

Published
2022

90. Stabilisation of a viscous conservation law by a one-dimensional external force

Author

Djurdjevac, Ana, Shirikyan, Armen, Shirikyan, Armen, Systèmes stochastiques et ouverts hors équilibre - - NONSTOPS2017 - ANR-17-CE40-0006 - AAPG2017 - VALID, PSI - - PSI2016 - ANR-16-IDEX-0008 - IDEX - VALID, and Modèles Mathématiques et Economiques de la Dynamique, de l'Incertitude et des Interactions - - MME-DII2011 - ANR-11-LABX-0023 - LABX - VALID

Subjects
exponential stabilisation, one-dimensional control, Mathematics - Analysis of PDEs, Optimization and Control (math.OC), FOS: Mathematics, approximate controllability, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], 35L65, 35Q93, 35R60, 93C20, viscous conservation law, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Optimization and Control, Analysis of PDEs (math.AP)
Abstract

We study a damped scalar conservation law driven by the sum of a fixed external force and a localised one-dimensional control. The problem is considered in a bounded domain and is supplemented with the Dirichlet boundary condition. It is proved that any solution of the uncontrolled equation can be exponentially stabilised. As a consequence, we obtain the global approximate controllability to trajectories by a one-dimensional localised control., 20 pages

Published
2022

91. Personalized incentives as feedback design in generalized Nash equilibrium problems

Author

Fabiani, Filippo, Simonetto, Andrea, Goulart, Paul J., and Simonetto, Andrea

Subjects
FOS: Computer and information sciences, Computer Science::Computer Science and Game Theory, Computer Science - Machine Learning, TheoryofComputation_GENERAL, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, Machine Learning (cs.LG), Optimization and Control (math.OC), Computer Science - Computer Science and Game Theory, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Mathematics - Optimization and Control, Computer Science and Game Theory (cs.GT)
Abstract

We investigate both stationary and time-varying, nonmonotone generalized Nash equilibrium problems that exhibit symmetric interactions among the agents, which are known to be potential. As may happen in practical cases, however, we envision a scenario in which the formal expression of the underlying potential function is not available, and we design a semi-decentralized Nash equilibrium seeking algorithm. In the proposed two-layer scheme, a coordinator iteratively integrates the (possibly noisy and sporadic) agents' feedback to learn the pseudo-gradients of the agents, and then design personalized incentives for them. On their side, the agents receive those personalized incentives, compute a solution to an extended game, and then return feedback measurements to the coordinator. In the stationary setting, our algorithm returns a Nash equilibrium in case the coordinator is endowed with standard learning policies, while it returns a Nash equilibrium up to a constant, yet adjustable, error in the time-varying case. As a motivating application, we consider the ridehailing service provided by several companies with mobility as a service orchestration, necessary to both handle competition among firms and avoid traffic congestion, which is also adopted to run numerical experiments verifying our results., arXiv admin note: text overlap with arXiv:2111.03854

Published
2022

92. An optimal feedback control that minimizes the epidemic peak in the SIR model under a budget constraint

Author

Emilio Molina, Alain Rapaport, Rapaport, Alain, Departamento de Ingeniería Matemática [Santiago] (DIM), Universidad de Chile = University of Chile [Santiago] (UCHILE)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPC), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPC)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPC), Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Institut Agro Montpellier, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), ANID-PFCHA/Doctorado Nacional/2018-21180348 (Chile), FONDECYT grant 1201982 (Chile), ACE210010 and FB210005, BASAL funds for center of excellence, ANID Chile, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Center for Mathematical Modeling (CMM), Universidad de Chile = University of Chile [Santiago] (UCHILE), and Departamento de Ingeniera Matematica [Santiago] (DIM)

Subjects
Maximum cost, Epidemiology, digestive, oral, and skin physiology, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Feedback control, Optimal control, [SDV.SPEE] Life Sciences [q-bio]/Santé publique et épidémiologie, Control and Systems Engineering, Optimization and Control (math.OC), FOS: Mathematics, Quantitative Biology::Populations and Evolution, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], SIR model, Electrical and Electronic Engineering, Mathematics - Optimization and Control
Abstract

International audience; We give the explicit solution of the optimal control problem which consists in minimizing the epidemic peak in the SIR model when the control is an attenuation factor of the infectious rate, subject to a L 1 constraint on the control which represents a budget constraint. The optimal strategy is given as a feedback control which consists in a singular arc maintaining the infected population at a constant level until the immunity threshold is reached, and no intervention outside the singular arc. We discuss and compare this strategy with the one that minimizes the peak when fixing the duration of a single intervention, as already proposed in the literature. Numerical simulations illustrate the benefits of the proposed control.

Published
2022

93. Exact boundary controllability of 1D semilinear wave equations through a constructive approach

Author

Kuntal Bhandari, Jérôme Lemoine, Arnaud Münch, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and Munch, Arnaud

Subjects
93B05 Semilinear wave equation, Control and Optimization, Control and Systems Engineering, Applied Mathematics, Signal Processing, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Fixed point, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Exact boundary controllability, Carleman estimates, AMS Classifications: 35L71
Abstract

The exact boundary controllability of the semilinear wave equation ytt − yxx + f (y) = 0, x ∈ (0, 1) assuming that f is locally Lipschitz continuous and satisfies the growth condition lim sup |r|→∞ |f (r)|/(|r| ln p |r|) β for some β small enough and p = 2 has been obtained by Zuazua in 1993. The proof based on a non constructive fixed point arguments makes use of precise estimates of the observability constant for a linearized wave equation. Under the above asymptotic assumption with p = 3/2, by introducing a different fixed point application, we present a simpler proof of the exact boundary controllability which is not based on the cost of observability of the wave equation with respect to potentials. Then, assuming that f is locally Lipschitz continuous and satisfies the growth condition lim sup |r|→∞ |f (r)|/ ln 3/2 |r| β for some β small enough, we show that the above fixed point application is contracting yielding a constructive method to approximate the controls for the semilinear equation. Numerical experiments illustrate the results. The results can be extended to the multi-dimensional case and for nonlinearities involving the gradient of the solution.

Published
2022

94. A hybrid approach combining cnns and variational modelling for blind image denoising

Author

Rekik Dit Nekhili, Rim, Descombes, Xavier, Calatroni, Luca, Capture and Analysis of Shapes in Motion (MORPHEO), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), and Calatroni, Luca

Subjects
[INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], Computer Science::Computer Vision and Pattern Recognition, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Image denoising, Convolutional Neural Networks, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Local hyperparameter estimation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Total Variation
Abstract

We consider the problem of image denoising with unknown noise distribution. We propose a hybrid approach where model-based space-variant total variation (TV) regularization is used for denoising with hyperparameters estimated locally using a Convolutional Neural Network (CNN) with a simple and light architecture. The special choice of the weighted TV prior allows for the use of a limited learning set, while the use of the proposed CNN approach allows for local parameter estimation independently of the type of noise in the data. The obtained results show that the proposed hybrid approach takes benefit from both the prior information encoded in the choice of the regularization model and the versatility of the CNN-based parameter estimation approach.

Published
2022

95. Mass concentration in rescaled first order integral functionals

Author

Monteil, Antonin, Pegon, Paul, Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), A. M. acknowledges support by Leverhulme grant RPG-2018-438., Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris, Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), and Pegon, Paul

Subjects
Relaxation, H-mass, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], semicontinuity, [MATH] Mathematics [math], convergence of measures, Functionals on measures, Mathematics - Analysis of PDEs, integral functionals, branched transport, Primary: 28A33, 49J45, 46E35, Secondary: 49Q20, 76T99, 49Q22, 49J10, Γ-convergence, Optimization and Control (math.OC), FOS: Mathematics, concentration-compactness, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH]Mathematics [math], Mathematics - Optimization and Control, Cahn-Hilliard fluids, Analysis of PDEs (math.AP), Calculus of variations
Abstract

We consider first order local minimization problems of the form $\min \int_{\mathbb{R}^N}f(u,\nabla u)$ under a mass constraint $\int_{\mathbb{R}^N}u=m\in\mathbb{R}$. We prove that the minimal energy function $H(m)$ is always concave on $(-\infty,0)$ and $(0,+\infty)$, and that relevant rescalings of the energy, depending on a small parameter $\varepsilon$, $\Gamma$-converge in the weak topology of measures towards the $H$-mass, defined for atomic measures $\sum_i m_i\delta_{x_i}$ as $\sum_i H(m_i)$. We also consider space dependent Lagrangians $f(x,u,\nabla u)$, which cover the case of space dependent $H$-masses $\sum_i H(x_i,m_i)$, and also the case of a family of Lagrangians $(f_\varepsilon)_\varepsilon$ converging as $\varepsilon\to 0$. The $\Gamma$-convergence result holds under mild assumptions on $f$, and covers several situations including homogeneous \(H\)-masses in any dimension $N\geq 2$ for exponents above a critical threshold, and all concave $H$-masses in dimension $N=1$. Our result yields in particular the concentration of Cahn-Hilliard fluids into droplets, and is related to the approximation of branched transport by elliptic energies.

Published
2022

96. Optimal sampled-data controls with running inequality state constraints: Pontryagin maximum principle and bouncing trajectory phenomenon

Author

Gaurav Dhar, Loïc Bourdin, Mathématiques & Sécurité de l'information (XLIM-MATHIS), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), and Dhar, Gaurav

Subjects
function of bounded variations, General Mathematics, Stieltjes integral, 0211 other engineering and technologies, [MATH] Mathematics [math], 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, digital control, [SPI.AUTO]Engineering Sciences [physics]/Automatic, optimal control, Variational principle, Pontryagin maximum principle, Applied mathematics, [MATH]Mathematics [math], 0101 mathematics, Mathematics, 021103 operations research, state constraints, Numerical analysis, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Riemann–Stieltjes integral, Ekeland variational principle, shooting method, Optimal control, indirect method, Nonlinear system, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Sampled-data control, Control system, Bounded function, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Riemann-Stieltjes integral, Software, Hamiltonian (control theory)
Abstract

International audience; Sampled-data control systems have steadily been gaining interest for their applications in automatic engineering where they are implemented as digital controllers and recently results have been obtained in optimal control theory for nonlinear sampled-data control systems and certain generalizations. In this paper we derive a Pontryagin maximum principle for general nonlinear finite-dimensional optimal sampled-data control problems with running inequality state constraints. In particular, we obtain a nonpositive averaged Hamiltonian gradient condition with the adjoint vector being a function of bounded variations. Our proof is based on the Ekeland variational principle. In general, optimal control problems with running inequality state constraints are difficult to solve using numerical methods due to the discontinuities (the jumps and the singular part) of the adjoint vector. However in our case we find that under certain general hypotheses the adjoint vector only experiences jumps at most at the sampling times and moreover the trajectory only contacts the running inequality state constraints at most at the sampling times. We call this behavior a bouncing trajectory phenomenon and it constitutes the second major focus of this paper. Finally taking advantage of the bouncing trajectory phenomenon we numerically solve three examples with different kinds of constraints and in several dimensions.

Published
2020

97. A new regularity criterion of weak solutions to the 3D micropolar fluid flows in terms of the pressure

Author

Maria Alessandra Ragusa, Michel Théra, Sadek Gala, Thera, Michel, University of Mostaganem, Mostaganem, Algeria, University of Catania [Italy], Université de Limoges (UNILIM), and Federation University Australia Ballarat

Subjects
General Mathematics, 010102 general mathematics, Mathematical analysis, Regularity, three-dimensional micropolar fluid flows. pressure field, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], 01 natural sciences, Pressure field, Regularity, Physics::Fluid Dynamics, three-dimensional micropolar fluid flows. pressure field, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics
Abstract

This note aims to giving a new regularity criterion for weak solutions to the three-dimensional micropolar fluid flows by imposing a critical growth condition on the field of pressure. Keywords Micropolar fluid flows; · weak solutions; · Pressure criterion · Besov spaces.. Mathematics Subject Classification (2000) 35Q35 · 35B65 · 76D05 In this note we consider the following Cauchy problem (1) for the incompressible micropolar fluid equations in R 3 : ∂ t u − ∆ u + (u · ∇) u + ∇π − ∇ × ω = 0, (1a) ∂ t ω − ∆ ω − ∇∇ · ω + 2ω + (u · ∇)ω − ∇ × u = 0, (1b) ∇ · u = 0, (1c) u(x, 0) = u 0 (x), ω(x, 0) = ω 0 (x), (1d) where u = u(x,t) ∈ R 3 , ω = ω(x,t) ∈ R 3 and π = π (x,t) denote the unknown velocity of the fluid, the micro-rotational velocity of the fluid particles and the unknown scalar pressure of the fluid at the point (x,t) ∈ R 3 × (0, T), respectively, while u 0 , ω 0 are given initial data satisfying ∇ · u = 0 in the sense of distributions. This model for micropolar fluid flows proposed by Eringen [6] enables to consider some physical phenomena that cannot be treated by the classical Navier-Stokes equations for the viscous incompressible fluids, such as for example, the motion of animal blood, muddy fluids, liquid crystals and dilute aqueous polymer solutions, colloidal suspensions, etc. When the micro-rotation effects are neglected or ω = 0, (1) reduces to the in-compressible Navier-Stokes equations, and it is well known that regularity criteria

Published
2020

98. Sampling from Non-smooth Distributions Through Langevin Diffusion

Author

Jalal M. Fadili, Christophe Chesneau, Tung Duy Luu, Normandie Université (NU), Equipe Image - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), and Fadili, Jalal

Subjects
Statistics and Probability, Mathematical optimization, Discretization, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, General Mathematics, media_common.quotation_subject, Context (language use), 01 natural sciences, 010104 statistics & probability, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Consistency (statistics), Applied mathematics, Simplicity, 0101 mathematics, Variational analysis, Diffusion (business), [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Mathematics, media_common, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], 010102 general mathematics, Sampling (statistics), [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Regression analysis, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 16. Peace & justice, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In this paper, we propose proximal splitting-type algorithms for sampling from distributions whose densities are not necessarily smooth nor log-concave. Our approach brings together tools from, on the one hand, variational analysis and non-smooth optimization, and on the other hand, stochastic diffusion equations, and in particular the Langevin diffusion. We establish in particular consistency guarantees of our algorithms seen as discretization schemes in this context. These algorithms are then applied to compute the exponentially weighted aggregates for regression problems involving non-smooth penalties that are commonly used to promote some notion of simplicity/complexity. Some popular penalties are detailed and implemented on some numerical experiments.

Published
2020

99. Regret Lower Bounds for Unbiased Adaptive Control of Linear Quadratic Regulators

Author

Henrik Sandberg, Ingvar Ziemann, and Ziemann, Ingvar

Subjects
Sequential estimation, Control and Optimization, Adaptive control, Logarithm, MathematicsofComputing_NUMERICALANALYSIS, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Regret, Linear-quadratic regulator, Upper and lower bounds, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Scaling limit, Control and Systems Engineering, Convergence (routing), Applied mathematics, Mathematics
Abstract

We present lower bounds for the regret of adaptive control of the linear quadratic regulator. These are given in terms of problem specific expected regret lower bounds valid for unbiased policies linear in the state. Our approach is based on the insight that the adaptive control problem can, given our assumptions, be reduced to a sequential estimation problem. This enables the use of the Cramer-Rao information inequality which yields a scaling limit lower bound of logarithmic order. The bound features both information-theoretic and control-theoretic quantities. By leveraging existing results, we are able to show that the bound is tight in a special case.

Published
2020

100. Stabilization of a rigid body moving in a compressible viscous fluid

Author

Takéo Takahashi, Arnab Roy, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Takahashi, Takéo

Subjects
Viscous liquid, 01 natural sciences, Damper, Mathematics - Analysis of PDEs, Mathematics (miscellaneous), Position (vector), Fluid-structure interaction, Fluid–structure interaction, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Ball (mathematics), [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Mathematics, 010102 general mathematics, Mathematical analysis, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Rigid body, MSC : 35Q35, 35D30, 35D35, 35R37, 76N10, 93D15, 93D20, compressible Navier-Stokes system, stabilization, 010101 applied mathematics, Spring (device), Compressibility, global solutions, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Analysis of PDEs (math.AP)
Abstract

We consider the stabilizability of a fluid-structure interaction system where the fluid is viscous and compressible and the structure is a rigid ball. The feedback control of the system acts on the ball and corresponds to a force that would be produced by a spring and a damper connecting the center of the ball to a fixed point $$h_1$$ . We prove the global-in-time existence of strong solutions for the corresponding system under a smallness condition on the initial velocities and on the distance between the initial position of the center of the ball and $$h_1$$ . Then, we show with our feedback law, that the fluid and the structure velocities go to 0 and that the center of the ball goes to $$h_1$$ as $$t\rightarrow \infty $$ .

Published
2020

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