A new modified approximate proximal-extragradient type method for monotone variational inequalities

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...

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 ...

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

On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean

In this paper we analyze the iteration-complexity of the hybrid proximal extragradient (HPE) method for finding a zero of a maximal monotone operator recently proposed by Solodov and Svaiter. One of the key points of our analysis is the use of a new termination criteria based on the εenlargement of a maximal monotone operator. The advantages of using this termination criterion it that its defin...

An inexact alternating direction method with SQP regularization for the structured variational inequalities

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...