AN ADAPTIVE TRUST-REGION METHOD FOR GENERALIZED EIGENVALUES OF SYMMETRIC TENSORS

作     者：Yuting Chen Mingyuan Cao Yueting Yang Qingdao Huang Yuting Chen;Mingyuan Cao;Yueting Yang;Qingdao Huang

作者机构：School of MathematicsJilin UniversityChangchun 130012China School of Mathematics and StatisticsBeihua UniversityJilin 132013China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2021年第39卷第3期

页      面：358-374页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported in part by the NNSF of China(11171003) the Innovation Talent Training Program of Science and Technology of Jilin Province of China(20180519011JH) the Science and Technology Development Project Program of Jilin Province(20190303132SF) The research of Mingyuan Cao is partially supported by the Project of Education Department of Jilin Province(JJKH20200028KJ) The research of Qingdao Huang is partially supported by the NNSF of China(11171131). 

主　　题：Symmetric tensors Generalized eigenvalues Trust-region Global convergence Local quadratic convergence 

摘      要：For symmetric tensors,computing generalized eigenvalues is equivalent to a homogenous polynomial optimization over the unit sphere.In this paper,we present an adaptive trustregion method for generalized eigenvalues of symmetric tensors.One of the features is that the trust-region radius is automatically updated by the adaptive technique to improve the algorithm performance.The other one is that a projection scheme is used to ensure the feasibility of all iteratives.Global convergence and local quadratic convergence of our algorithm are established,respectively.The preliminary numerical results show the efficiency of the proposed algorithm.