NEWTON’S METHOD FOR SOLVING THE GENERALIZED COMPLEMENTARITY PROBLEM

Abstract

The generalized complementarity problem is an extension of the standard complementarity problem. Traditional approaches often reformulate the GCP as nonsmooth nonlinear equations using nonsmooth NCP functions, and apply smoothing-type methods for solutions. In this paper, we propose an alternative approach by reformulating the GCP as a smooth nonlinear equation using a class of smooth NCP functions. This reformulation allows for the direct application of Newton's method to solve the obtained equation. Under specific conditions, we show that this approach has a quadratic convergence, and we give some numerical examples to illustrate the efficiency of this method.