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In infinite-dimensional Hilbert spaces we device a class of strongly convergent primal-dual schemes for solving variational inequalities defined by a Lipschitz continuous and pseudomonote map. Our novel numerical scheme is based on Tseng's…

Optimization and Control · Mathematics 2019-08-27 Benoit Duvocelle , Dennis Meier , Mathias Staudigl , Phan Tu Vuong

We propose an inertial variant of the strongly convergent inexact proximal-point (PP) method of Solodov and Svaiter (2000) for monotone inclusions. We prove strong convergence of our main algorithm under less restrictive assumptions on the…

Optimization and Control · Mathematics 2025-09-24 M. Marques Alves , J. E. Navarro Caballero , M. Geremia , R. T. Marcavillaca

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 investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…

Optimization and Control · Mathematics 2026-01-19 Pham Viet Hai , Thanh Quoc Trinh , Phan Tu Vuong

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 article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…

Optimization and Control · Mathematics 2023-11-10 Emilie Chouzenoux , Jean-Christophe Pesquet , Fernando Roldán

The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…

Optimization and Control · Mathematics 2023-08-02 S. S. Ablaev , F. S. Stonyakin , M. S. Alkousa , D. A. Pasechnyuk

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

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

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

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased…

Optimization and Control · Mathematics 2021-02-18 Nguyen Van Dung , Bang Cong Vu

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

Optimization and Control · Mathematics 2022-12-14 Thang Tran Ngoc , Hai Trinh Ngoc

In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results…

Numerical Analysis · Mathematics 2024-06-12 Antonio Leitão , Joel C. Rabelo , Dirk A. Lorenz , Maximilian Winkler

This paper introduces a family of stochastic extragradient-type algorithms for a class of nonconvex-nonconcave problems characterized by the weak Minty variational inequality (MVI). Unlike existing results on extragradient methods in the…

Optimization and Control · Mathematics 2023-02-20 Thomas Pethick , Olivier Fercoq , Puya Latafat , Panagiotis Patrinos , Volkan Cevher

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

This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…

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

Monotone variational inequalities (VIs) provide a unifying framework for convex minimization, equilibrium computation, and convex-concave saddle-point problems. Extragradient-type methods are among the most effective first-order algorithms…

Optimization and Control · Mathematics 2026-04-16 Lingqing Shen , Fatma Kılınç-Karzan

In this paper, we propose two parallel extragradient - viscosity methods for finding a particular element in the common solution set of a system of equilibrium problems and finitely many fixed point problems. This particular point is the…

Optimization and Control · Mathematics 2016-03-08 Dang Van Hieu

In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…

Optimization and Control · Mathematics 2019-02-25 J. Y. Bello Cruz , R. Díaz Millán , Hung M. Phan

We attempt to provide an algorithm for approximating a solution of the quasiconvex equilibrium problem that was proved to exist by K. Fan 1972. The proposed algorithm is an iterative procedure, where the search direction at each iteration…

Optimization and Control · Mathematics 2023-04-25 Le Hai Yen , Le Dung Muu