Error Bound and Convergence Analysis of Matrix Splitting Algorithms for the Affine Variational Inequality Problem

It is shown that the distance to a feasible point near the solution set can be bounded by the norm of a natural residual at that point, and this bound is used to prove linear convergence of a matrix splitting algorithm for solving the symmetric case of the affine variational inequality problem.

Abstract

Consider the affine variational inequality problem. It is shown that the distance to the solution set from a feasible point near the solution set can be bounded by the norm of a natural residual at that point. This bound is then used to prove linear convergence of a matrix splitting algorithm for solving the symmetric case of the problem. This latter result improves upon a recent result of Luo and Tseng that further assumes the problem to be monotone.