Search

In this paper we first present a novel operator extrapolation (OE) method for solving deterministic variational inequality (VI) problems. Similar to the gradient (operator) projection method, OE updates one single search sequence by solving a single projection subproblem in each iteration. We show that OE can achieve the optimal rate of convergence for solving a variety of VI problems in a much simpler way than existing approaches. We then introduce the stochastic operator extrapolation (SOE) method and establish its optimal convergence behavior for solving various stochastic VI problems. In particular, SOE achieves the optimal complexity for solving a fundamental problem, i.e., stochastic smooth and strongly monotone VI, for the first time in the literature. We also present a stochastic block operator extrapolation method to further reduce the iteration cost for the OE method applied to large-scale deterministic VIs with a certain block structure. Numerical experiments have been conducted to demonstrate the potential advantages of the proposed algorithms. In fact, all these algorithms are applied to solve generalized monotone variational inequality problems whose operator is not necessarily monotone. We will also discuss optimal OE-based policy evaluation methods for reinforcement learning in a companion paper. [ABSTRACT FROM AUTHOR]

This work addresses the finite-horizon robust covariance control problem for discrete time, partially observable, linear systems affected by random zero mean noise and deterministic uncertain-but-bounded disturbances restricted to lie in what is called ellitopic uncertainty set (e.g., finite intersection of centered at the origin ellipsoids/elliptic cylinders). Performance specifications are imposed on the random state-control trajectory via averaged convex quadratic inequalities, linear inequalities on the mean, chance constrained linear inequalities as well as convex-monotone constraints on the covariance matrix. For this problem we develop a computationally tractable procedure for designing affine control policies, in the sense that the parameters of the policy that guarantees the aforementioned performance specifications are obtained as solutions to an explicit convex program. Our theoretical findings are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

Optimizing the backwashing procedure of ultrafiltration membranes poses novel challenges in regards to the modeling and simulation of the fouling process. Traditional modeling approaches the problem through a physical and chemical understanding of the complicated fouling phenomena. In this study, a large amount of data has been collected from a pilot-scale ultrafiltration membrane system treating spent filter backwash water at a water treatment plant. Environmental variables and operational parameters including temperature, hydraulic pressure, water turbidity, etc. are monitored continuously. This work focuses on revealing the hidden nonlinear relationships of these variables via data driven methodologies without building a first principles process model. Machine learning tools are used to establish a connection between environmental variables, dynamic parameters, the efficiency of foulant removal through backwashing, and the increase rate of foulants. The prediction performance is compared to regression models including linear regression, artificial neural networks, and random forests. Our data driven model of the fouling dynamics is then used for optimization purposes, in particular, to optimize the backwashing sequence timing by applying tools from stochastic dynamic programming. Optimized backwash performance is compared with experimental data acquired via a fixed interval sequence and shows a more efficient schedule at less cost and with lower membrane resistance. This work establishes a full pipeline of data processing, model building, and operational optimization. The only requirement for employing our methodology is the collection of operational data, in order to identify the membrane dynamics. The reported methodology offers a great potential for implementation on large-scale ultrafiltration applications, which can improve energy consumption and elongate membrane life. Image 1 • Full pipeline of data analysis and dynamical parameter modeling have been developed. • Machine learning models and operational optimization are integrated. • A Markov decision model was used to describe UF membrane resistance evolution. • Backwash performance has been improved on both energy cost and membrane health. [ABSTRACT FROM AUTHOR]