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

摘要

Consider the affine variational inequality problem. It is shown that the distanceto 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. Affine variational inequality, linear complemtarity, error bound, matrix splitting, linear convergence.