Limited Memory BFGS Method for Least Squares Semidefinite Programming with Banded Structure  

作　　者：XUE Wenjuan SHEN Chungen YU Zhensheng 

机构地区：[1]School of Mathematics and Physics,Shanghai University of Electric Power,Shanghai,200090,China [2]University of Shanghai for Science and Technology,Shanghai,200093,China

出　　处：《Journal of Systems Science & Complexity》2022年第4期1500-1519,共20页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.11601318。

摘　　要：This work is intended to solve the least squares semidefinite program with a banded structure. A limited memory BFGS method is presented to solve this structured program of high dimension.In the algorithm, the inverse power iteration and orthogonal iteration are employed to calculate partial eigenvectors instead of full decomposition of n × n matrices. One key feature of the algorithm is that it is proved to be globally convergent under inexact gradient information. Preliminary numerical results indicate that the proposed algorithm is comparable with the inexact smoothing Newton method on some large instances of the structured problem.

关 键 词：Banded structure inexact gradient least squares semidefinite program limited memory BFGS orthogonal iteration 

分 类 号：O22[理学—运筹学与控制论]