A new smoothing method for nonlinear complementarity problems involving P0 function

TL;DR

This paper introduces a novel smoothing method for nonlinear complementarity problems involving P0-functions, featuring a nonparametric algorithm with convergence guarantees and efficient numerical performance.

Contribution

It presents a new smoothing approach with a variable regularization parameter, eliminating complex update strategies and improving solution efficiency.

Findings

The method converges globally and locally.

Numerical experiments demonstrate high efficiency.

Applications show practical effectiveness.

Abstract

In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local convergence results. We also present several numerical experiments and applications that show the efficiency of our approach. Our main contribution relies in the fact that the regularization parameter r is considered as a variable and we do not need any complicated strategy to update it.