Tensor eigenvalue complementarity problems

• 成果类型: Article
• 署名作者: Fan, Jinyan; Nie, Jiawang; Zhou, Anwa
• 署名单位: Shanghai Jiao Tong University; Shanghai Jiao Tong University; University of California System; University of California San Diego; Shanghai University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1167-y
• 发表日期: 2018
• 页码: 507-539
• 关键词: elastic-systems; unilateral contact; optimization; STABILITY; POLYNOMIALS

摘要

This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial optimization. When one tensor is strictly copositive, the complementarity eigenvalues can be computed by solving polynomial optimization with normalization by strict copositivity. When no tensor is strictly copositive, we formulate the tensor eigenvalue complementarity problem equivalently as polynomial optimization by a randomization process. The complementarity eigenvalues can be computed sequentially. The formulated polynomial optimization can be solved by Lasserre's hierarchy of semidefinite relaxations. We show that it has finite convergence for generic tensors. Numerical experiments are presented to show the efficiency of proposed methods.