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11 results on '"Adil M. Bagirov"'

1. Nonsmooth Optimization-Based Hyperparameter-Free Neural Networks for Large-Scale Regression

Author

Napsu Karmitsa, Sona Taheri, Kaisa Joki, Pauliina Paasivirta, Adil M. Bagirov, and Marko M. Mäkelä

Subjects
machine learning, regression analysis, neural networks, L1-loss function, nonsmooth optimization, Industrial engineering. Management engineering, T55.4-60.8, Electronic computers. Computer science, QA75.5-76.95
Abstract

In this paper, a new nonsmooth optimization-based algorithm for solving large-scale regression problems is introduced. The regression problem is modeled as fully-connected feedforward neural networks with one hidden layer, piecewise linear activation, and the L1-loss functions. A modified version of the limited memory bundle method is applied to minimize this nonsmooth objective. In addition, a novel constructive approach for automated determination of the proper number of hidden nodes is developed. Finally, large real-world data sets are used to evaluate the proposed algorithm and to compare it with some state-of-the-art neural network algorithms for regression. The results demonstrate the superiority of the proposed algorithm as a predictive tool in most data sets used in numerical experiments.

Published
2023
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2. Bundle Enrichment Method for Nonsmooth Difference of Convex Programming Problems

Author

Manlio Gaudioso, Sona Taheri, Adil M. Bagirov, and Napsu Karmitsa

Subjects
DC optimization, nonconvex nonsmooth optimization, cutting plane, bundle method, Industrial engineering. Management engineering, T55.4-60.8, Electronic computers. Computer science, QA75.5-76.95
Abstract

The Bundle Enrichment Method (BEM-DC) is introduced for solving nonsmooth difference of convex (DC) programming problems. The novelty of the method consists of the dynamic management of the bundle. More specifically, a DC model, being the difference of two convex piecewise affine functions, is formulated. The (global) minimization of the model is tackled by solving a set of convex problems whose cardinality depends on the number of linearizations adopted to approximate the second DC component function. The new bundle management policy distributes the information coming from previous iterations to separately model the DC components of the objective function. Such a distribution is driven by the sign of linearization errors. If the displacement suggested by the model minimization provides no sufficient decrease of the objective function, then the temporary enrichment of the cutting plane approximation of just the first DC component function takes place until either the termination of the algorithm is certified or a sufficient decrease is achieved. The convergence of the BEM-DC method is studied, and computational results on a set of academic test problems with nonsmooth DC objective functions are provided.

Published
2023
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3. The non-smooth and bi-objective team orienteering problem with soft constraints

Author

Adil M. Bagirov, Angel A. Juan, Albert Ferrer, Alejandro Estrada-Moreno, Javier Panadero, Universitat Oberta de Catalunya (UOC), Universitat Oberta de Catalunya. Internet Interdisciplinary Institute (IN3), Universitat Rovira i Virgili, Universitat Politècnica de Catalunya, Euncet Business School, and Federation University

Subjects
biased-randomized algorithms, Mathematical optimization, Biased-randomized algorithms, Computer science, General Mathematics, media_common.quotation_subject, 0211 other engineering and technologies, Orienteering, restricciones suaves, Algorismes, 02 engineering and technology, Multi-objective optimization, team orienteering problem, optimització multiobjectiu, Programació orientada a objectes (Informàtica), 0202 electrical engineering, electronic engineering, information engineering, Computer Science (miscellaneous), Range (statistics), Soft constraints, Team orienteering problem, Function (engineering), Driving range, Engineering (miscellaneous), media_common, algoritmos sesgados-aleatorios, 021103 operations research, Algoritmos, soft constraints, algoritmes esbiaixats-aleatoris, lcsh:Mathematics, optimización multiobjetivo, optimización no suave, lcsh:QA1-939, optimització no suau, Constraint (information theory), restriccions suaus, multi-objective optimization, Order (business), 020201 artificial intelligence & image processing, problema d'orientació de l'equip, Routing (electronic design automation), problema de orientación del equipo, non-smooth optimization, Algorithms, Matemàtiques i estadística::Investigació operativa::Optimització [Àrees temàtiques de la UPC]
Abstract

In the classical team orienteering problem (TOP), a fixed fleet of vehicles is employed, each of them with a limited driving range. The manager has to decide about the subset of customers to visit, as well as the visiting order (routes). Each customer offers a different reward, which is gathered the first time that it is visited. The goal is then to maximize the total reward collected without exceeding the driving range constraint. This paper analyzes a more realistic version of the TOP in which the driving range limitation is considered as a soft constraint: every time that this range is exceeded, a penalty cost is triggered. This cost is modeled as a piece-wise function, which depends on factors such as the distance of the vehicle to the destination depot. As a result, the traditional reward-maximization objective becomes a non-smooth function. In addition, a second objective, regarding the design of balanced routing plans, is considered as well. A mathematical model for this non-smooth and bi-objective TOP is provided, and a biased-randomized algorithm is proposed as a solving approach.

Published
2020

4. Double Bundle Method for finding Clarke Stationary Points in Nonsmooth DC Programming

Author

Marko M. Mäkelä, Sona Taheri, Napsu Karmitsa, Adil M. Bagirov, and Kaisa Joki

Subjects
021103 operations research, ta111, 0211 other engineering and technologies, Regular polygon, Dc programming, 010103 numerical & computational mathematics, 02 engineering and technology, Bundle methods, 01 natural sciences, Stationary point, Theoretical Computer Science, Double bundle, Applied mathematics, Computer Science::Symbolic Computation, 0101 mathematics, Software, Mathematics
Abstract

The aim of this paper is to introduce a new proximal double bundle method for unconstrained nonsmooth optimization, where the objective function is presented as a difference of two convex (DC) func...

Published
2018

5. New diagonal bundle method for clustering problems in large data sets

Author

Adil M. Bagirov, Napsu Karmitsa, and Sona Taheri

Subjects
Clustering high-dimensional data, ta112, 021103 operations research, Information Systems and Management, Fuzzy clustering, General Computer Science, Correlation clustering, ta111, 0211 other engineering and technologies, Constrained clustering, 02 engineering and technology, Management Science and Operations Research, computer.software_genre, Industrial and Manufacturing Engineering, Data stream clustering, CURE data clustering algorithm, Modeling and Simulation, 0202 electrical engineering, electronic engineering, information engineering, Canopy clustering algorithm, 020201 artificial intelligence & image processing, Data mining, Cluster analysis, computer, Mathematics
Abstract

Clustering is one of the most important tasks in data mining. Recent developments in computer hardware allow us to store in random access memory (RAM) and repeatedly read data sets with hundreds of thousands and even millions of data points. This makes it possible to use conventional clustering algorithms in such data sets. However, these algorithms may need prohibitively large computational time and fail to produce accurate solutions. Therefore, it is important to develop clustering algorithms which are accurate and can provide real time clustering in large data sets. This paper introduces one of them. Using nonsmooth optimization formulation of the clustering problem the objective function is represented as a difference of two convex (DC) functions. Then a new diagonal bundle algorithm that explicitly uses this structure is designed and combined with an incremental approach to solve this problem. The method is evaluated using real world data sets with both large number of attributes and large number of data points. The proposed method is compared with two other clustering algorithms using numerical results.

Published
2017

6. Partitional Clustering Via Nonsmooth Optimization : Clustering Via Optimization

Author

Adil M. Bagirov, Napsu Karmitsa, Sona Taheri, Adil M. Bagirov, Napsu Karmitsa, and Sona Taheri

Subjects
Nonsmooth optimization
Abstract

This book describes optimization models of clustering problems and clustering algorithms based on optimization techniques, including their implementation, evaluation, and applications. The book gives a comprehensive and detailed description of optimization approaches for solving clustering problems; the authors'emphasis on clustering algorithms is based on deterministic methods of optimization. The book also includes results on real-time clustering algorithms based on optimization techniques, addresses implementation issues of these clustering algorithms, and discusses new challenges arising from big data. The book is ideal for anyone teaching or learning clustering algorithms. It provides an accessible introduction to the field and it is well suited for practitioners already familiar with the basics of optimization.

Published
2020

7. Numerical Nonsmooth Optimization : State of the Art Algorithms

Author

Adil M. Bagirov, Manlio Gaudioso, Napsu Karmitsa, Marko M. Mäkelä, Sona Taheri, Adil M. Bagirov, Manlio Gaudioso, Napsu Karmitsa, Marko M. Mäkelä, and Sona Taheri

Subjects
Nonsmooth optimization
Abstract

Solving nonsmooth optimization (NSO) problems is critical in many practical applications and real-world modeling systems. The aim of this book is to survey various numerical methods for solving NSO problems and to provide an overview of the latest developments in the field. Experts from around the world share their perspectives on specific aspects of numerical NSO. The book is divided into four parts, the first of which considers general methods including subgradient, bundle and gradient sampling methods. In turn, the second focuses on methods that exploit the problem's special structure, e.g. algorithms for nonsmooth DC programming, VU decomposition techniques, and algorithms for minimax and piecewise differentiable problems. The third part considers methods for special problems like multiobjective and mixed integer NSO, and problems involving inexact data, while the last part highlights the latest advancements in derivative-free NSO. Given its scope, the book isideal for students attending courses on numerical nonsmooth optimization, for lecturers who teach optimization courses, and for practitioners who apply nonsmooth optimization methods in engineering, artificial intelligence, machine learning, and business. Furthermore, it can serve as a reference text for experts dealing with nonsmooth optimization.

Published
2020

10. An incremental piecewise linear classifier based on polyhedral conic separation

Author

Adil M. Bagirov, Refail Kasimbeyli, Gurkan Ozturk, Anadolu Üniversitesi, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümü, and Kasımbeyli, Refail

Subjects
Mathematical optimization, Discrete Gradient Method, Classification, Piecewise linear function, Nonlinear system, Error function, Discrete gradient method, Artificial Intelligence, Conic section, Nonsmooth Nonconvex Optimization, A priori and a posteriori, Polyhedral Conic Separation, Classifier (UML), Software, ComputingMethodologies_COMPUTERGRAPHICS, Mathematics
Abstract

WOS: 000361624700018, In this paper, a piecewise linear classifier based on polyhedral conic separation is developed. This classifier builds nonlinear boundaries between classes using polyhedral conic functions. Since the number of polyhedral conic functions separating classes is not known a priori, an incremental approach is proposed to build separating functions. These functions are found by minimizing an error function which is nonsmooth and nonconvex. A special procedure is proposed to generate starting points to minimize the error function and this procedure is based on the incremental approach. The discrete gradient method, which is a derivative-free method for nonsmooth optimization, is applied to minimize the error function starting from those points. The proposed classifier is applied to solve classification problems on 12 publicly available data sets and compared with some mainstream and piecewise linear classifiers., Australian Research Council [DP140103213], The authors would like to thank three anonymous referees for their criticism and comments which allowed to improve the quality of the paper. The research by Dr. A.M. Bagirov was supported under Australian Research Council's Discovery Projects funding scheme (Project No. DP140103213).

Published
2015

11. Piecewise linear classifiers based on nonsmooth optimization approaches

Author

Adil M. Bagirov, Julien Ugon, Refail Kasimbeyli, Gurkan Ozturk, Anadolu Üniversitesi, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümü, and Kasımbeyli, Refail

Subjects
Piecewise linear function, Mathematical optimization, ComputingMethodologies_PATTERNRECOGNITION, Optimization algorithm, Computer science, Efficient algorithm, Conic section, Data classification
Abstract

Nonsmooth optimization provides efficient algorithms for solving many machine learning problems. In particular, nonsmooth optimization approaches to supervised data classification problems lead to the design of very efficient algorithms for their solution. In this chapter, we demonstrate how nonsmooth optimization algorithms can be applied to design efficient piecewise linear classifiers for supervised data classification problems. Such classifiers are developed using a max–min and a polyhedral conic separabilities as well as an incremental approach. We report results of numerical experiments and compare the piecewise linear classifiers with a number of other mainstream classifiers.

Published
2014

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