Quadratic tensor eigenvalue complementarity problems

Ruixue Zhao; Jinyan Fan

doi:10.3934/jimo.2022073

Article Contents

2023, Volume 19, Issue 4: 2986-3002. Doi: 10.3934/jimo.2022073

This issue Previous Article Optimal pricing strategy in a dual-channel supply chain: A two-period game analysis Next Article A bi-level optimization model for the asset-liability management of insurance companies

Quadratic tensor eigenvalue complementarity problems

Ruixue Zhao^1, , and
Jinyan Fan^2,

1.
School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China
2.
School of Mathematical Sciences, Key Lab of Scientific and Engineering Computing (Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, China

^*Corresponding author: Ruixue Zhao
^*Corresponding author: Ruixue Zhao

Received: October 2021

Revised: March 2022

Published: April 2023

The first author is supported by the Science and Technology Commission of Shanghai Municipality grant 22YF1412400, the second author is supported by NSFC grant 11971309

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Abstract

In this paper, we study the quadratic tensor eigenvalue complementarity problem (QTEiCP). By a randomization process, the quadratic complementarity(QC) eigenvalues are classified into two cases. For each case, the QTEiCP is formulated as an equivalent generalized moment problem. The QC eigenvectors can be computed in order. Each of them can be solved by a sequence of semidefinite relaxations. We prove that such a sequence converges in finitely many steps for generic tensors.

Keywords:

Quadratic tensor eigenvalue complementarity problem,
moment problem,
polynomial reformulations,
Lasserre's semidefinite relaxation,
finite convergence.

Mathematics Subject Classification: 65K10, 15A18, 65F15, 90C22.

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