A sub-additive DC approach to the complementarity problem

Abstract

In this article, we propose a new merit function based on sub-additive functions for solving a general complementarity problem. This leads to consider an optimization problem that is equivalent to the NCP. In the case of a concave NCP this optimization problem is a Difference of Convex (DC) program and we can therefore use DC Algorithm to locally solve it. We prove that in the case of a monotone NCP, it is sufficient to compute a stationary point of the optimization problem to get a solution of the complementarity problems. In the case of a general NCP, assuming that a DC decomposition of the complementarity problem is known, we propose a penalization technique to reformulate the optimization problem as a DC program. Numerical results on linear complementarity problems and absolute value equations show that our method is promising.