Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems

TL;DR

This paper introduces a novel homotopy function based on KKT conditions to efficiently solve linear complementarity problems, extending applicability and overcoming limitations of previous methods.

Contribution

It proposes a new homotopy approach rooted in KKT conditions, enhancing the solution process for a broader class of linear complementarity problems.

Findings

Homotopy path is smooth and bounded.

The proposed algorithm is effective and superior to existing methods.

Numerical examples demonstrate the approach's efficiency.

Abstract

In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose homotopy functions based on original problems. We propose the homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem. The proposed approach extends the processability of the larger class of linear complementarity problem and overcomes the limitations of other existing homotopy approaches. We show that the homotopy path approaching the solution is smooth and bounded with positive tangent direction of the homotopy path. Various classes of numerical examples are illustrated to show the effectiveness of the proposed algorithm and the superiority of the algorithm among other existing iterative methods.