Smoothing Methods for Nonlinear Complementarity Problems

TL;DR

This paper introduces a new smoothing method for solving nonlinear complementarity problems, providing theoretical convergence results and demonstrating efficiency through numerical tests.

Contribution

The paper presents a novel smoothing approach with proven convergence and error estimates for nonlinear complementarity problems under general conditions.

Findings

Proven convergence under $P_0$ condition.

Established error estimates with new monotonicity conditions.

Numerical tests confirm method efficiency.

Abstract

In this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate under a new and general monotonicity condition. The numerical tests confirm the efficiency of our proposed methods.