A New Approach for Solving the Linear Complementarity Problem using Smoothing Functions

TL;DR

This paper introduces two novel smoothing-based methods, TLCP and Soft-Max, for solving linear complementarity problems, inspired by interior-point techniques, with improved parameter management and validated through extensive numerical testing.

Contribution

The paper presents two new smoothing methods for LCP that eliminate complex parameter updates and demonstrate strong theoretical and empirical performance.

Findings

Methods outperform classical approaches in numerical tests

No need for complex smoothing parameter management

Theoretical convergence guarantees provided

Abstract

Based on smoothing techniques, we propose two new methods to solve linear complementarity problems (LCP) called TLCP and Soft-Max. The idea of these two new methods takes inspiration from interior-point methods in optimization. The technique that we propose avoids any parameter management while ensuring good theoretical convergence results. In our approach we do not need any complicated strategy to update the smoothing parameter r since we will consider it as a new variable. Our methods are validated by extensive numerical tests, in which we compare our methods to several other classical methods.