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We consider variational inequalities coming from monotone operators, a setting that includes convex minimization and convex-concave saddle-point problems. We assume an access to potentially noisy unbiased values of the monotone operators…

Machine Learning · Computer Science 2019-02-06 Francis Bach , Kfir Y. Levy

This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…

Optimization and Control · Mathematics 2025-06-04 Mohammad S. Alkousa , Belal A. Alashqar , Fedor S. Stonyakin , Tarek Nabhani , Seydamet S. Ablaev

The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz…

Optimization and Control · Mathematics 2022-05-25 F. S. Stonyakin , A. A. Titov , D. V. Makarenko , M. S. Alkousa

We introduce an inexact oracle model for variational inequalities (VI) with monotone operator, propose a numerical method which solves such VI's and analyze its convergence rate. As a particular case, we consider VI's with…

Optimization and Control · Mathematics 2022-02-18 Fedor Stonyakin , Alexander Gasnikov , Pavel Dvurechensky , Mohammad Alkousa , Alexander Titov

Basing on some recently proposed methods for solving variational inequalities with non-smooth operators, we propose an analogue of the Mirror Prox method for the corresponding class of problems under the assumption of relative smoothness…

Optimization and Control · Mathematics 2021-06-09 Alexander A. Titov

We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…

Machine Learning · Computer Science 2021-08-30 Alina Ene , Huy L. Nguyen

We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…

Machine Learning · Statistics 2022-02-24 Nuri Mert Vural , Lu Yu , Krishnakumar Balasubramanian , Stanislav Volgushev , Murat A. Erdogdu

This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…

Optimization and Control · Mathematics 2025-11-11 Vladimir Solodkin , Andrew Veprikov , Aleksandr Beznosikov

In this paper we propose new algorithms for solving a class of structured monotone variational inequality (VI) problems over compact feasible sets. By identifying the gradient components existing in the operator of VI, we show that it is…

Optimization and Control · Mathematics 2021-11-02 Guanghui Lan , Yuyuan Ouyang

The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…

Optimization and Control · Mathematics 2023-11-22 Alexander Titov , Fedor Stonyakin , Mohammad Alkousa , Alexander Gasnikov

In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…

Optimization and Control · Mathematics 2022-11-01 A. A. Titov , S. S. Ablaev , M. S. Alkousa , F. S. Stonyakin , A. V. Gasnikov

In this paper we consider iterative methods for stochastic variational inequalities (s.v.i.) with monotone operators. Our basic assumption is that the operator possesses both smooth and nonsmooth components. Further, only noisy observations…

Optimization and Control · Mathematics 2011-06-01 Anatoli Juditsky , Arkadii S. Nemirovskii , Claire Tauvel

Mirror-prox (MP) is a well-known algorithm to solve variational inequality (VI) problems. VI with a monotone operator covers a large group of settings such as convex minimization, min-max or saddle point problems. To get a convergent…

Machine Learning · Computer Science 2020-11-24 Reza Babanezhad , Simon Lacoste-Julien

Some adaptive analogue of the Mirror Prox method for variational inequalities is proposed. In this work we consider the adaptation not only to the value of the Lipschitz constant, but also to the magnitude of the oracle error. This…

Optimization and Control · Mathematics 2020-03-27 Fedor Stonyakin , Evgeniya Vorontsova , Mohammad Alkousa

In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…

In this paper we present an inexact proximal point method for variational inequality problem on Hadamard manifolds and study its convergence properties. The proposed algorithm is inexact in two sense. First, each proximal subproblem is…

Optimization and Control · Mathematics 2021-03-04 G. C. Bento , O. P. Ferreira , E. A. Papa Quiroz

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…

Machine Learning · Statistics 2016-08-15 Mohammad Emtiyaz Khan , Reza Babanezhad , Wu Lin , Mark Schmidt , Masashi Sugiyama

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

A new adaptive approach is proposed for variational inequalities with a Lipschitz-continuous field. Estimates of the necessary number of iterations are obtained to achieve a given quality of the variational inequality solution. A…

Optimization and Control · Mathematics 2018-12-27 Fedor Stonyakin , Alexander Gasnikov , Pavel Dvurechensky , Alexander Titov

Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…

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