Optimality Conditions for Rank-Constrained Matrix Optimization  

作　　者：Xin-Rong Li Wen Song Nai-Hua Xiu 

机构地区：[1]Department of Applied Mathematics,Beijing Jiaotong University,Beijing 100044,China [2]School of Mathematical Sciences,Harbin Normal University,Harbin 150025,China

出　　处：《Journal of the Operations Research Society of China》2019年第2期285-301,共17页中国运筹学会会刊（英文）

基　　金：This research was supported by the National Natural Science Foundation of China(Nos.11431002 and 11371116).

摘　　要：In this paper,we comprehensively study optimality conditions for rank-constrained matrix optimization(RCMO).By calculating the Clarke tangent and normal cones to a rank-constrained set,along with the given Fréchet,Mordukhovich normal cones,we investigate four kinds of stationary points of the RCMO and analyze the relations between each stationary point and local/global minimizer of the RCMO.Furthermore,the second-order optimality condition of the RCMO is achieved with the help of the Clarke tangent cone.

关 键 词：Matrix optimization Rank constraint Normal cone First-order optimality condition Second-order optimality condition 

分 类 号：O17[理学—数学]