On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators

Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems

Abstract. We propose a prox-type method with efficiency estimate O(2−1) for approximating saddle points of convex-concave C1,1 functions and solutions of variational inequalities with monotone Lipschitz continuous operators. Application examples include matrix games, eigenvalue minimization and computing Lovasz capacity number of a graph and are illustrated by numerical experiments with large-s...

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...

Projected Reflected Gradient Methods for Monotone Variational Inequalities

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 constant stepsize. It is similar to the projected gradient method, namely, the method requires only one projection onto the feasible set and only one value of the ...

Pii: S0893-9659(01)00137-9

Keywords--Variat ional inequalities, Projection method, Fixed point, Convergence. 1. I N T R O D U C T I O N Variational inequalities.have had a great impact and influence in the development of almost all branches of pure and applied sciences. There are a substantial number of numerical methods including projection, the WieneroHopf equations, auxiliary principle techniques for solving variation...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points