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This paper seeks to address how to solve non-smooth convex and strongly convex optimization problems with functional constraints. The introduced Mirror Descent (MD) method with adaptive stepsizes is shown to have a better convergence rate…

Optimization and Control · Mathematics 2017-05-08 Anastasia Bayandina

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Optimization and Control · Mathematics 2019-07-18 Mostafa Amini , Farzad Yousefian

We investigate different randomizations for mirror descent method. We try to propose such a randomization that allows us to use sparsity of the problem as much as it possible. In the paper one can also find a generalization of randomizaed…

Optimization and Control · Mathematics 2016-12-12 Anton Anikin , Alexander Gasnikov , Alexander Gornov

In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning. Our…

Optimization and Control · Mathematics 2021-07-06 Waïss Azizian , Franck Iutzeler , Jérôme Malick , Panayotis Mertikopoulos

We consider minimizing a sum of non-smooth objective functions with set constraints in a distributed manner. As to this problem, we propose a distributed algorithm with an exponential convergence rate for the first time. By the exact…

Optimization and Control · Mathematics 2020-01-06 Weijian Li , Xianlin Zeng , Shu Liang , Yiguang Hong

Mirror descent is a well established tool for solving convex optimization problems with convex constraints. This article introduces continuous-time mirror descent dynamics for approximating optimal Markov controls for stochastic control…

Optimization and Control · Mathematics 2025-06-04 Deven Sethi , David Šiška

In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional constraints are considered. It is shown that the methods are…

Optimization and Control · Mathematics 2018-12-20 F. S. Stonyakin , M . S. Alkousa , A. A. Titov

An open problem in optimization with noisy information is the computation of an exact minimizer that is independent of the amount of noise. A standard practice in stochastic approximation algorithms is to use a decreasing step-size. This…

Optimization and Control · Mathematics 2021-02-24 Anastasia Borovykh , Nikolas Kantas , Panos Parpas , Grigorios A. Pavliotis

The paper is devoted to a special Mirror Descent algorithm for problems of convex minimization with functional constraints. The objective function may not satisfy the Lipschitz condition, but it must necessarily have the Lipshitz-continuous…

Optimization and Control · Mathematics 2018-04-17 Fedor S. Stonyakin , Alexander A. Titov

This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…

Optimization and Control · Mathematics 2013-07-09 Angelia Nedich , Soomin Lee

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Optimization and Control · Mathematics 2020-01-22 Mohammad S. Alkousa

We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…

Statistics Theory · Mathematics 2007-06-13 Anatoli Juditsky , Alexander Nazin , Alexandre Tsybakov , Nicolas Vayatis

We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as…

Optimization and Control · Mathematics 2012-08-02 John C. Duchi , Alekh Agarwal , Mikael Johansson , Michael I. Jordan

We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and…

Optimization and Control · Mathematics 2023-07-11 Dai Hai Nguyen , Tetsuya Sakurai

We consider the problem of minimizing the sum of non-smooth convex functions in non-Euclidean spaces, e.g., probability simplex, via only local computation and communication on an undirected graph. We propose two algorithms motivated by…

Optimization and Control · Mathematics 2019-08-22 Yue Yu , Behçet Açıkmeşe , Mehran Mesbahi

Learning-to-optimize is an emerging framework that leverages training data to speed up the solution of certain optimization problems. One such approach is based on the classical mirror descent algorithm, where the mirror map is modelled…

Optimization and Control · Mathematics 2023-06-05 Hong Ye Tan , Subhadip Mukherjee , Junqi Tang , Andreas Hauptmann , Carola-Bibiane Schönlieb

Inspired by the recent paper (L. Ying, Mirror descent algorithms for minimizing interacting free energy, Journal of Scientific Computing, 84 (2020), pp. 1-14),we explore the relationship between the mirror descent and the variable metric…

Optimization and Control · Mathematics 2021-06-28 Li Wang , Ming Yan

We consider distributed optimization with smooth convex objective functions defined on an undirected connected graph. Inspired by mirror descent mehod and RLC circuits, we propose a novel distributed mirror descent method. Compared with…

Optimization and Control · Mathematics 2020-02-25 Yue Yu , Behçet Açıkmeşe

The part of the analysis of the convergence rate of the mirror descent method that is connected with the adaptive time-varying step size rules due to Alkousa et al. (MOTOR 2024, pp. 3-18) is corrected. Moreover, a Lipschitz-free mirror…

Optimization and Control · Mathematics 2025-06-03 Bowen Yuan , Mohammad S. Alkousa

This paper is concerned with multi-agent optimization problem. A distributed randomized gradient-free mirror descent (DRGFMD) method is developed by introducing a randomized gradient-free oracle in the mirror descent scheme where the…

Optimization and Control · Mathematics 2019-03-12 Zhan Yu , Daniel W. C. Ho , Deming Yuan