Error Bound and Convergence Analysis of Matrix Splitting Algorithms for the Affine Variational Inequality Problem
Zhi-Quan Tom Luo, Paul Tseng · SIAM Journal on Optimization · 1992
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.