Lagrangian Globalization method together with new NCP-functions for the Nonlinear Complementarity Problem

Abstract

無中文摘要

In this paper, we look into the detailed properties of six NCP-functions. Based on these NCP functions, we present a Lagrangian globalization (LG) algorithm model for solving the nonlinear complementarity problem. In particular, this algorithm model does not depend on some specific NCP function. Under several theoretical assumptions on NCP functions. We prove that the algorithm model is well-defined. Several NCP functions applicable to the LG-method are analyzed in details and shown to satisfy these assumptions. Furthermore, we identify not only the properties of NCP functions which enable them to be used in the LG method but also their properties which enable the strict complementarity condition to be removed from the convergence conditions of the LG method.