A New Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem

Abstract

Based on the smoothing NCP function, we first reformulate the generalized nonlinear complementarity problem over a polyhedral cone as a smoothing system of equations, and then propose a new smoothing inexact Newton method for solving it. In each iteration, the corresponding linear system is solved only inexact solution. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. For the proposed method, we also obtain its global convergence under weaker conditions, and we further establish its local super linear(quadratic) convergence under the BD-regular assumption.