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We propose an inertial forward-backward splitting algorithm to compute the zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in…

Optimization and Control · Mathematics 2015-07-06 Lorenzo Rosasco , Silvia Villa , Bang Cong Vu

The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a…

Optimization and Control · Mathematics 2019-05-27 Yura Malitsky

In this paper we study the bounded perturbation resilience of projection and contraction algorithms for solving variational inequality (VI) problems in real Hilbert spaces. Under typical and standard assumptions of monotonicity and…

Optimization and Control · Mathematics 2017-11-20 Qiao-Li Dong , Aviv Gibali , Dan Jiang , Shang-Hong Ke

In this paper, a scalable iterative projection-type algorithm for solving non-stationary systems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and…

Mathematical Software · Computer Science 2020-08-24 Leonid B. Sokolinsky , Irina M. Sokolinskaya

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

In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the…

Optimization and Control · Mathematics 2020-08-31 Bing Tan , Zheng Zhou , Xiaolong Qin

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…

Optimization and Control · Mathematics 2020-08-31 Zheng Zhou , Bing Tan , Songxiao Li

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 an inertial Tseng's extragradient method for solving multi-valued variational inequalits, in which only one projection is needed at each iterate. We also obtain the strong convergence results of the proposed…

Optimization and Control · Mathematics 2020-11-26 Changjie Fang , Ruirui Zhang , Shenglan Chen

In this paper, we study inclusion problems where the involved operators may not be monotone in the classical sense. Specifically, we assume the operators to be generalized monotone, a weaker notion than classical monotonicity. This allows…

Optimization and Control · Mathematics 2025-03-12 Nam Van Tran

In this paper an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and studied its convergence properties. The main tool used for presenting the method is the concept of enlargement of monotone…

Optimization and Control · Mathematics 2015-11-30 E. E. A. Batista , G. C. Bento , O. P. Ferreira

Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…

Machine Learning · Computer Science 2026-05-19 Mohammad S. Alkousa , Fedor S. Stonyakin , Belal A. Alashqar , Seydamet S. Ablaev

Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…

Optimization and Control · Mathematics 2022-10-28 Patrick L. Combettes , Jean-Christophe Pesquet , Audrey Repetti

We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…

Optimization and Control · Mathematics 2022-06-14 Ahmet Alacaoglu , Yura Malitsky

In this paper, we study a class of generalized inverse mixed variational inequality problems (GIMVIPs). We propose a novel projection-based second-order time-varying dynamical system for solving GIMVIPs. Under the assumptions that the…

Optimization and Control · Mathematics 2026-01-23 Nam Van Tran

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…

Optimization and Control · Mathematics 2011-09-14 Q. Tran Dinh , C. Savorgnan , M. Diehl

The 2-sets convex feasibility problem aims at finding a point in the nonempty intersection of two closed convex sets $A$ and $B$ in a Hilbert space $X$. The method of alternating projections is the simplest iterative procedure for finding a…

Optimization and Control · Mathematics 2020-06-29 Carlo A. De Bernardi , Enrico Miglierina

In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing…

Optimization and Control · Mathematics 2013-11-13 Cong D. Dang , Guanghui Lan

In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates…

Dynamical Systems · Mathematics 2024-06-28 Oday Hazaimah

We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…

Numerical Analysis · Mathematics 2021-01-28 Andreas Dedner , Alice Hodson