A semidefinite method for tensor complementarity problems. (4th July 2019)

• Record Type: Journal Article
• Authors: Zhao, Xin; Fan, Jinyan
• Is Part Of: Optimization methods and software. Volume 34:Number 4(2019)
• Page Start: 758
• Page End: 769
• Publication Date: 2019-07-04
• Subjects: tensor complementarity problem -- polynomial optimization -- semidefinite relaxation; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1439489
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we study how to compute all real solutions of the tensor complimentary problem, if there are finite many ones. We formulate the problem as a sequence of polynomial optimization problems. The solutions can be computed sequentially. Each of them can be obtained by solving Lasserre's hierarchy of semidefinite relaxations. A semidefinite algorithm is proposed and its convergence properties are discussed. Some numerical experiments are also presented.