A modified subgradient extragradient method for solving monotone variational inequalities

Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces

In this paper, we combine the subgradient extragradient method with the Halpern method for finding a solution of a variational inequality involving a monotone Lipschitz mapping in Banach spaces. By using the generalized projection operator and the Lyapunov functional introduced by Alber, we prove a strong convergence theorem. We also consider the problem of finding a common element of the set o...

The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space

We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

A Hybrid Proximal Extragradient Self-Concordant Primal Barrier Method for Monotone Variational Inequalities

In this paper we present a primal interior-point hybrid proximal extragradient (HPE) method for solving a monotone variational inequality over a closed convex set endowed with a selfconcordant barrier and whose underlying map has Lipschitz continuous derivative. In contrast to the method of [7] in which each iteration required an approximate solution of a linearized variational inequality over ...

Iteration-Complexity of a Newton Proximal Extragradient Method for Monotone Variational Inequalities and Inclusion Problems

In a recent paper by Monteiro and Svaiter, a hybrid proximal extragradient (HPE) framework was used to study the iteration-complexity of a first-order (or, in the context of optimization, second-order) method for solving monotone nonlinear equations. The purpose of this paper is to extend this analysis to study a prox-type first-order method for monotone smooth variational inequalities and incl...