Improved DC Programming Approaches for Solving the Quadratic Eigenvalue Complementarity Problem

TL;DR

This paper introduces improved difference of convex programming methods for solving the Quadratic Eigenvalue Complementarity Problem, leading to faster convergence and higher solution precision through a novel local dc decomposition.

Contribution

It proposes a new local dc decomposition tailored for QEiCP, enhancing the efficiency and accuracy of DC algorithms compared to existing approaches.

Findings

Faster convergence of the proposed dc algorithms.

Higher solution precision achieved with the new decomposition.

Numerical results demonstrate practical efficiency.

Abstract

In this paper, we discuss the solution of a Quadratic Eigenvalue Complementarity Problem (QEiCP) by using Difference of Convex (DC) programming approaches. We first show that QEiCP can be represented as dc programming problem. Then we investigate different dc programming formulations of QEiCP and discuss their dc algorithms based on a well-known method -- DCA. A new local dc decomposition is proposed which aims at constructing a better dc decomposition regarding to the specific feature of the target problem in some neighborhoods of the iterates. This new procedure yields faster convergence and better precision of the computed solution. Numerical results illustrate the efficiency of the new dc algorithms in practice.