Pseudomonotone Variational Inequalities Research Articles

Fast alternated inertial projection algorithms for pseudo-monotone variational inequalities

In this paper, we propose an alternated inertial subgradient extragradient algorithm for variational inequalities with self-adaptive step-sizes and obtain weak and linear convergence results. We also obtain linear convergence results using an alternated inertial projected gradient algorithm for which knowledge of the modulus of strong pseudo-monotonicity and Lipschitz constant of the cost function are not needed. We compare numerically our algorithms with other projection-type algorithms in the literature.

An inertial subgradient-extragradient algorithm for solving pseudomonotone variational inequalities

An inertial subgradient-extragradient algorithm for solving pseudomonotone variational inequalities

Revisiting the extragradient method for finding the minimum-norm solution of non-Lipschitzian pseudo-monotone variational inequalities

Revisiting the extragradient method for finding the minimum-norm solution of non-Lipschitzian pseudo-monotone variational inequalities

An inertia-based algorithm for pseudomonotone variational inequality and fixed point problems in real Hilbert space

The aim of this work is to study a pseudomonotone variational inequality and a fixed point problem involving pseudocontractive mappings in real Hilbert spaces. We introduce an inertia-based iterative algorithm for finding a common solution to this problem. The strong convergence of the proposed algorithm is proved. Finally, numerical examples are provided and also meaningful comparisons of these results with those in [Y. Yao, M. Postolache, J. C. Yao, Mathematics, \(\textbf{7}\) (2019), 14 pages], proving that at our proposed numerical schemes are more efficient.

Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems

Abstract In this paper, we study the problem of finding a common solution of the pseudomonotone variational inequality problem and fixed point problem for demicontractive mappings. We introduce a new inertial iterative scheme that combines Tseng’s extragradient method with the viscosity method together with the adaptive step size technique for finding a common solution of the investigated problem. We prove a strong convergence result for our proposed algorithm under mild conditions and without prior knowledge of the Lipschitz constant of the pseudomonotone operator in Hilbert spaces. Finally, we present some numerical experiments to show the efficiency of our method in comparison with some of the existing methods in the literature.

Convergence theorems for solving a system of pseudomonotone variational inequalities using Bregman distance in Banach spaces

Convergence theorems for solving a system of pseudomonotone variational inequalities using Bregman distance in Banach spaces

Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications

Inertial extragradient algorithms with non-monotone stepsizes for pseudomonotone variational inequalities and applications

MODIFIED PROJECTION ALGORITHMS FOR STRONGLY PSEUDOMONOTONE VARIATIONAL INEQUALITIES

The variational inequality problem have many important applications in the fields of signal processing, image processing, optimal control and many others. In this paper, we introduce two projection algorithms for solving strongly pseudomonotone variational inequalities. The considered methodsare based on some existing ones. Our algorithms use dynamicstep-sizes, chosen based on information of previous steps andtheir strong convergence is proved without the Lipschitz continuity of the underlying mappings. Some numerical experiments are presented to verify the effectiveness of the proposedalgorithms.

ON THE STRONG CONVERGENCE FOR ITERATIVE METHODS TO FIND A SOLUTION OF A SPLIT PSEUDOMONOTONE VARIATIONAL INEQUALITY AND A SPLIT FEASIBILITY PROBLEM

In this paper, we introduce two different interative methods for finding a solution of a split pseudomonotone variational inequality and a split feasibility problem in Hilbert spaces. The proposed algorithm is generated based on the subgradient extragradient method which requires only two projections at each iteration step and the second projection is conducted onto the half-space containing the constrained set. The strong convergence is proven with some mild conditions imposed on the operators as well as the parameters. A numerical result is provided at the end of the paper with the use of Python for the convergence illustration purpose of the studied method.

On Strengthened Inertial-Type Subgradient Extragradient Rule with Adaptive Step Sizes for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive Mappings

In a real Hilbert space, let the VIP denote a pseudomonotone variational inequality problem with Lipschitz continuity operator, and let the CFPP indicate a common fixed-point problem of finitely many nonexpansive mappings and an asymptotically nonexpansive mapping. On the basis of the Mann iteration method, the viscosity approximation method and the hybrid steepest-descent method, we propose and analyze two strengthened inertial-type subgradient extragradient rules with adaptive step sizes for solving the VIP and CFPP. With the help of suitable restrictions, we show the strong convergence of the suggested rules to a common solution of the VIP and CFPP, which is the unique solution of a hierarchical variational inequality (HVI).

"Extragradient method with a new adaptive step size for solving non-Lipschitzian pseudo-monotone variational inequalities"

"The purpose of this work is to develop a new version of the extragradient method for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. First, we prove a sufficient condition for weak convergence of a proposed algorithm under relaxed assumptions. Next, under strong pseudomonotonicity and Lipschitz continuity assumptions, we obtain also a Q-linear convergence rate of this algorithm. Our results improve some recent contributions in the literature on the extragradient method."

Modified Mann Subgradient-like Extragradient Rules for Variational Inequalities and Common Fixed Points Involving Asymptotically Nonexpansive Mappings

In a real Hilbert space, we aim to investigate two modified Mann subgradient-like methods to find a solution to pseudo-monotone variational inequalities, which is also a common fixed point of a finite family of nonexpansive mappings and an asymptotically nonexpansive mapping. We obtain strong convergence results for the sequences constructed by these proposed rules. We give some examples to illustrate our analysis.

Projection and Contraction Methods for Solving Bilevel Pseudomonotone Variational Inequalities

Projection and Contraction Methods for Solving Bilevel Pseudomonotone Variational Inequalities

A strong convergence algorithm for solving pseudomonotone variational inequalities with a single projection

A strong convergence algorithm for solving pseudomonotone variational inequalities with a single projection

Inertial Viscosity Iterative Method for Solving Pseudo-monotone Variational Inequality Problems and Fixed Point Problems

Inertial Viscosity Iterative Method for Solving Pseudo-monotone Variational Inequality Problems and Fixed Point Problems

Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators

Two projection-based methods for bilevel pseudomonotone variational inequalities involving non-Lipschitz operators

Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities

Global and linear convergence of alternated inertial single projection algorithms for pseudo-monotone variational inequalities

Strong convergence of an iterative procedure for pseudomonotone variational inequalities and fixed point problems

Pseudomonotone variational inequalities have been investigated by many authors, a common assumption ?weak sequential continuity? being imposed on pseudomonotone operators. In this paper, we propose an iterative procedure for solving pseudomonotone variational inequalities and fixed point problems of asymptotically pseudocontractive operators by using self-adaptive techniques. Under a weaker assumption than weak sequential continuity imposed on pseudomonotone operators, we prove that the suggested procedure has strong convergence.

Inertial method for split null point problems with pseudomonotone variational inequality problems

<p style='text-indent:20px;'>This paper analyzed the new extragradient type algorithm with inertial extrapolation step for solving self adaptive split null point problem and pseudomonotone variational inequality in real Hilbert space. Furthermore, in this study, a strong convergence result is obtained without assuming Lipschitz continuity of the associated mapping and the operator norm is self adaptive. Additionally, the proposed algorithm only uses one projections onto the feasible set in each iteration. More so, the strong convergence results are obtained under some relaxed conditions on the initial factor and the iterative parameters. Numerical results are presented to illustrate the performance of the proposed algorithm.The results obtained in this study improved and extended related studies in the literature.</p>

A strong convergence theorem for solving pseudo-monotone variational inequalities and fixed point problems using subgradient extragradient method in Banach spaces

<abstract><p>In this paper, we introduce an algorithm for solving variational inequalities problem with Lipschitz continuous and pseudomonotone mapping in Banach space. We modify the subgradient extragradient method with a new and simple iterative step size, and the strong convergence to a common solution of the variational inequalities and fixed point problems is established without the knowledge of the Lipschitz constant. Finally, a numerical experiment is given in support of our results.</p></abstract>