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

作　　者：Yuting Chen Mingyuan Cao Yueting Yang Qingdao Huang 

机构地区：[1]School of Mathematics,Jilin University,Changchun 130012,China [2]School of Mathematics and Statistics,Beihua University,Jilin 132013,China

出　　处：《Journal of Computational Mathematics》2021年第3期358-374,共17页计算数学（英文）

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).

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.

关 键 词：Symmetric tensors Generalized eigenvalues TRUST-REGION Global convergence Local quadratic convergence 

分 类 号：O17[理学—数学]