A new smoothing-type algorithm for nonlinear weighted complementarity problem

Abstract

In this paper we study the nonlinear weighted complementarity problem (denoted by NWCP). We first introduce a smoothing function which can be used to reformulate the NWCP as a system of smooth nonlinear equations. Then we propose a new smoothing-type algorithm to solve the NWCP which adopts a nonmonotone line search scheme. In each iteration, our algorithm solves one linear system of equations and performs one line search. Under suitable assumptions, we prove that the proposed algorithm is globally and locally quadratically convergent. Some numerical results are reported.