A Smoothing-Type Algorithm for Solving Monotone Weighted Complementarity Problems

Abstract

Abstract The weighted complementarity problem is an extension of the standard finite dimensional complementarity problem. It is well known that the smoothing-type algorithm is a powerful tool of solving the standard complementarity problem. In this paper, we propose a smoothing-type algorithm for solving the weighted complementarity problem with a monotone function, which needs only to solve one linear system of equations and performs one line search at each iteration. We show that the proposed method is globally convergent under the assumption that the problem is solvable. The preliminary numerical results indicate that the proposed method is effective and robust for solving the monotone weighted complementarity problem.