The Sparse Solution to $\mathcal{KS}$-Tensor Complementarity Problems

TL;DR

This paper addresses finding sparse solutions to KS-tensor complementarity problems by transforming them into polynomial programming problems and applying SQP algorithms, demonstrating effective results through numerical experiments.

Contribution

It introduces a novel approach to solve KS-tensor complementarity problems using polynomial programming and SQP, overcoming nonconvexity challenges.

Findings

SQP effectively finds sparse solutions

Transformation into polynomial programming is feasible

Numerical results validate the approach

Abstract

In view of the KS-tensor complementarity problem, the sparse solution of this problem is studied. Due to the nonconvexity and noncontinuity of the l_0-norm, it is a NP hard problem to find the sparse solution of the KS-tensor complementarity problem. In order to solve this problem, we transform it into a polynomial programming problem with constraints. Then we use the sequential quadratic programming (SQP) algorithm to solve this transformed problem. Numerical results show that the SQP algorithm can find the sparse solutions of the KS-tensor complementarity problem effectively.