• 论文 •

### 核范数和谱范数下广义Sylvester方程最小二乘问题的一类改进算法

1. 南京师范大学数学科学学院, 南京 210023
• 收稿日期:2018-03-07 出版日期:2018-12-15 发布日期:2018-11-20
• 通讯作者: 徐玲玲,Email:xulingling@njnu.edu.cn
• 基金资助:

国家自然科学基金（No：11401314）.

Cai Wenyin, Xu Lingling. AN IMPROVED ALGORITHM FOR LEAST SQUARES PROBLEM OF GENERALIZED SYLVESTER EQUATION UNDER NUCLEAR NORM AND SPECTRAL NORM[J]. Mathematica Numerica Sinica, 2018, 40(4): 387-401.

### AN IMPROVED ALGORITHM FOR LEAST SQUARES PROBLEM OF GENERALIZED SYLVESTER EQUATION UNDER NUCLEAR NORM AND SPECTRAL NORM

Cai Wenyin, Xu Lingling

1. Nanjing Normal University, School of Mathematical Sciences, Nanjing 210023, China
• Received:2018-03-07 Online:2018-12-15 Published:2018-11-20

minXS||Σi=1NAiXBi-C||

In the paper[10], the authors discussed the numerical method solving generalized Sylvester equation least square problems with the nuclear norm and spectral norm:
minXS||Σi=1NAiXBi-C||
,where XS is a closed convex set. They used inexact alternating direction method in combination with threshold algorithm, Moreau - Yosida regularization algorithm, spectrum projection algorithm,LSQR algorithm and SPG algorithm. Based on[10], we introduce a new variable and use the alternating direction method to simplify the algorithm. Each subproblem can be solved exactly. More important, each variable has its own explicit solution expression. We prove the convergence of the proposed algorithm. The numerical tests show that the improved algorithm can be improved greatly in both time and iteration.

MR(2010)主题分类:

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