A hierarchy of semidefinite relaxations for completely positive tensor optimization problems

作     者：Zhou, Anwa Fan, Jinyan 

作者机构：Shanghai Univ Dept Math Shanghai 200444 Peoples R China Shanghai Jiao Tong Univ Sch Math Sci Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ MOE LSC Shanghai 200240 Peoples R China 

出 版 物：《JOURNAL OF GLOBAL OPTIMIZATION》 (全局最优化杂志)

年 卷 期：2019年第75卷第2期

页      面：417-437页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：NSFC [11701356, 11571234] National Postdoctoral Program for Innovative Talents Grant [BX201600097] China Postdoctoral Science Foundation [2016M601562] 

主　　题：CP tensor program Best CP tensor approximation Linear optimization with moments Nonnegative decomposition Semidefinite program 

摘      要：In this paper, we study the completely positive (CP) tensor program, which is a linear optimization problem with the cone of CP tensors and some linear constraints. We reformulate it as a linear program over the cone of moments, then construct a hierarchy of semidefinite relaxations for solving it. We also discuss how to find a best CP approximation of a given tensor. Numerical experiments are presented to show the efficiency of the proposed methods.