A class of second-order cone eigenvalue complementarity problems for higher-order tensors

TL;DR

This paper introduces reformulations of the second-order cone tensor eigenvalue complementarity problem, enabling better analysis and solution methods, with preliminary numerical results supporting the theoretical developments.

Contribution

It presents three reformulations of SOCTEiCP, including variational inequality and nonlinear programming models, facilitating analysis and solver development.

Findings

Equivalence to variational inequality under certain conditions

Reformulation as nonlinear programming problems for symmetric cases

Preliminary numerical results verify theoretical models

Abstract

In this paper, we consider the second-order cone tensor eigenvalue complementarity problem (SOCTEiCP) and present three different reformulations to the model under consideration. Specifically, for the general SOCTEiCP, we first show its equivalence to a particular variational inequality under reasonable conditions. A notable benefit is that such a reformulation possibly provides an efficient way for the study of properties of the problem. Then, for the symmetric and sub-symmetric SOCTEiCPs, we reformulate them as appropriate nonlinear programming problems, which are extremely beneficial for designing reliable solvers to find solutions of the considered problem. Finally, we report some preliminary numerical results to verify our theoretical results.