Solution of Tensor Complementarity Problem Using Homotopy Function

TL;DR

This paper introduces a new homotopy continuation method with a smooth, bounded path to efficiently solve tensor complementarity problems, a subclass of nonlinear complementarity issues involving tensors.

Contribution

It proposes a novel homotopy function and develops a continuation method specifically designed for tensor complementarity problems, demonstrating effectiveness through numerical examples.

Findings

Effective solution method for tensor complementarity problems

Smooth, bounded homotopy path improves convergence

Numerical examples validate the proposed approach

Abstract

The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a tensor. We propose a new homotopy function with smooth and bounded homotopy path to obtain solution of the tensor complementarity problem under some conditions. A homotopy continuation method is developed based on the proposed homotopy function. Several numerical examples are provided to show the effectiveness of the proposed homotopy continuation method.