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This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a…

Optimization and Control · Mathematics 2018-03-26 Yu. Malitsky

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

In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or…

Optimization and Control · Mathematics 2015-01-30 Yu. V. Malitsky , V. V. Semenov

This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic $O(1/n)$ convergence rate of our proposed algorithm in…

Optimization and Control · Mathematics 2022-07-21 Olaniyi S. Iyiola , Yekini Shehu

The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…

Optimization and Control · Mathematics 2024-06-24 R. Díaz Millán , O. P. Ferreira , J. Ugon

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

This paper studies the behavior of the extragradient algorithm [Korpelevich, 1976] when applied to hypomonotone operators, a class of problems that extends beyond the classical monotone setting. To support the understanding of this…

Optimization and Control · Mathematics 2025-01-20 Khaled Alomar , Tatjana Chavdarova

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

Optimization and Control · Mathematics 2011-01-10 Luis M. Briceño-Arias

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, 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

This paper introduces a subgradient extragradient algorithm with a conjugate gradient-type direction to solve pseudomonotone variational inequality problems in Hilbert spaces. The algorithm features a self-adaptive strategy that eliminates…

Optimization and Control · Mathematics 2025-05-07 Ibrahim Arzuka , Parin Chaipunya , Poom Kumam

In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories,…

Optimization and Control · Mathematics 2022-10-20 AÏcha Balhag , Zakaria Mazgouri , Michel Théra

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

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 introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…

Optimization and Control · Mathematics 2017-11-29 Regina S. Burachik , R. Díaz Millán

In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly…

Functional Analysis · Mathematics 2016-11-01 Zeynab Jouymandi , Fridoun Moradlou

In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…

Optimization and Control · Mathematics 2015-10-28 Dang Van Hieu

We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact…

Optimization and Control · Mathematics 2024-06-24 Ewa Bednarczuk , Giovanni Bruccola , Gabriele Scrivanti , The Hung Tran

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

This study explores an inertial-based contraction-type approach for addressing monotone variational inclusion problems (in short, MVIP) within real Hilbert spaces. Most contraction-type techniques assume Lipschitz continuity and…

Optimization and Control · Mathematics 2026-04-09 Feeroz Babu , Syed Shakaib Irfan , Jen-Chih Yao , Xiaopeng Zhao