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

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...

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

An Approximate Proximal Point Algorithm for Maximal Monotone Inclusion Problems

This paper presents and analyzes a strongly convergent approximate proximal point algorithm for finding zeros of maximal monotone operators in Hilbert spaces. The proposed method combines the proximal subproblem with a more general correction step which takes advantage of more information on the existing iterations. As applications, convex programming problems and generalized variational inequa...

Regularized HPE-Type Methods for Solving Monotone Inclusions with Improved Pointwise Iteration-Complexity Bounds

This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the standard HPE method applied to regularizations of the original MIP. It is shown that its pointwise iteration-complexity considerably improves the one of the H...