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This paper extends split variational inclusion problems to dynamic, stochastic, and multi-agent systems in Banach spaces. We propose novel iterative algorithms to handle stochastic noise, time-varying operators, and coupled variational…

Optimization and Control · Mathematics 2025-05-13 Saeed Hashemi Sababe , Ehsan Lotfali Ghasab

In this paper, we discuss variational inequality (VI) problems without monotonicity from the perspective of convergence of projection-type algorithms. In particular, we identify existing conditions as well as present new conditions that are…

Optimization and Control · Mathematics 2023-04-11 Kevin Huang , Shuzhong Zhang

We consider stochastic optimization problems where data is drawn from a Markov chain. Existing methods for this setting crucially rely on knowing the mixing time of the chain, which in real-world applications is usually unknown. We propose…

Machine Learning · Computer Science 2023-07-14 Ron Dorfman , Kfir Y. Levy

Variational Inequality (VI) problems have attracted great interest in the machine learning (ML) community due to their application in adversarial and multi-agent training. Despite its relevance in ML, the oft-used strong-monotonicity and…

Optimization and Control · Mathematics 2024-02-09 Daniil Vankov , Angelia Nedich , Lalitha Sankar

This paper considers stochastic monotone variational inequalities whose feasible region is the intersection of a (possibly infinite) number of convex functional level sets. A projection-based approach or direct Lagrangian-based techniques…

Optimization and Control · Mathematics 2025-10-20 Abhishek Chakraborty , Angelia Nedić

This paper focuses on non-monotone stochastic variational inequalities (SVIs) that may not have a unique solution. A commonly used efficient algorithm to solve VIs is the Popov method, which is known to have the optimal convergence rate for…

Optimization and Control · Mathematics 2025-10-17 Daniil Vankov , Angelia Nedich , Lalitha Sankar

In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…

Optimization and Control · Mathematics 2023-04-18 Aleksandr Beznosikov , Alexander Gasnikov , Karina Zainulina , Alexander Maslovskiy , Dmitry Pasechnyuk

In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods…

Optimization and Control · Mathematics 2026-03-18 Novel Kumar Dey , Mohammad Mahdi Ahmadi , Erfan Yazdandoost Hamedani , Afrooz Jalilzadeh

We study monotone variational inequalities that can arise as optimality conditions for constrained convex optimisation or convex-concave minimax problems and propose a novel algorithm that uses only one gradient/operator evaluation and one…

Optimization and Control · Mathematics 2023-07-24 Michael Sedlmayer , Dang-Khoa Nguyen , Radu Ioan Bot

In this paper, we propose an Anderson-accelerated stochastic extragradient algorithm for solving a class of stochastic variational inequalities, by incorporating Anderson acceleration into the stochastic extragradient method under a…

Optimization and Control · Mathematics 2026-05-27 Xin Qu , Wei Bian , Xiaojun Chen

We consider distributed stochastic variational inequalities (VIs) on unbounded domains with the problem data that is heterogeneous (non-IID) and distributed across many devices. We make a very general assumption on the computational network…

In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…

Optimization and Control · Mathematics 2020-12-02 Rui Gao , Filip Tronarp , Simo Särkkä

The main purpose of this paper is to propose a variance-based Bregman extragradient algorithm with line search for solving stochastic variational inequalities, which is robust with respect an unknown Lipschitz constant. We prove the almost…

Optimization and Control · Mathematics 2022-08-31 Xian-Jun Long , Yue-Hong He , Nan-Jing Huang

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

This paper establishes the convergence properties of the Popov mirror-prox algorithm for solving stochastic and deterministic variational inequalities (VIs) under a polynomial growth condition on the mapping variation. Unlike existing…

Optimization and Control · Mathematics 2025-10-21 Abhishek Chakraborty , Angelia Nedić

We consider the stochastic variational inequality problem in which the map is expectation-valued in a component-wise sense. Much of the available convergence theory and rate statements for stochastic approximation schemes are limited to…

Optimization and Control · Mathematics 2019-11-25 Aswin Kannan , Uday V. Shanbhag

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

We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…

Numerical Analysis · Mathematics 2020-06-09 Xiaobing Feng , Andreas Prohl , Liet Vo

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…

Optimization and Control · Mathematics 2018-01-15 Shuoguang Yang , Mengdi Wang , Ethan X. Fang

This paper deals with stochastic optimization problems involving Markovian noise with a zero-order oracle. We present and analyze a novel derivative-free method for solving such problems in strongly convex smooth and non-smooth settings…

Optimization and Control · Mathematics 2026-01-06 Boris Prokhorov , Semyon Chebykin , Alexander Gasnikov , Aleksandr Beznosikov