Tracing homotopy path for the solution of nonlinear complementarity Problem

TL;DR

This paper introduces a new homotopy continuation method for solving nonlinear complementarity problems, demonstrating smooth and bounded solution paths with an application to oligopoly equilibrium problems.

Contribution

A novel homotopy function is proposed for nonlinear complementarity problems, ensuring smooth solution trajectories and improved computational effectiveness.

Findings

Homotopy paths are proven to be smooth and bounded.

Numerical example confirms the method's effectiveness.

Application to oligopoly equilibrium demonstrates practical utility.

Abstract

In this article, we consider nonlinear complementarity problem. We introduce a new homotopy function for finding the solution of nonlinear complementarity problem through the trajectory . We show that the homotopy path approaching the solution is smooth and bounded . Numerical example of an oligopoly equilibrium problem is illustrated to show the effectiveness of the proposed algorithm. Keywords: Nonlinear complementarity problem, homotopy continuation method, Oligopoly equilibrium problem.