A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem

Abstract

Based on the smoothing function of penalized Fischer‐Burmeister NCP‐function, we propose a new smoothing inexact Newton algorithm with non‐monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic) convergence of the proposed algorithm under the BD‐regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.