列正交约束下广义Sylvester方程极小化问题的有效算法  

An Effective Algorithm for Generalized Sylvester Equation Minimization Problem Under Columnwise Orthogonal Constraints

作　　者：刘月园 王凯 秦树娟 李姣芬 Liu Yueyuan;Wang Kai;Qin Shujuan;Li Jiaofen(School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Guangxi Key Laboratory of Automatic Detecting Technology and Instruments,Guangxi Guilin 541004)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西高校数据分析与计算重点实验室&广西自动检测技术与仪器重点实验室,广西桂林541004

出　　处：《数学物理学报（A辑）》2021年第2期479-495,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(11761024,11561015,11961012);桂林电子科技大学院级研究生优秀学位论文培育项目(2019YJSPY03);院级研究生创新项目(2020YJSCX02);广西自然科学基金(2017GXNSFBA198082)。

摘　　要：研究列正交约束下广义Sylvester方程极小化问题的有效算法.基于Stiefel流形的几何性质和欧氏空间中的MPRP共轭梯度法,构造一类黎曼MPRP共轭梯度迭代求解算法,给出算法全局收敛性.该迭代格式得到的搜索方向总能保证该目标函数下降.数值实验和数值比较验证所提出算法对于问题模型是高效可行的.This paper presents an efficient algorithm for solving the generalized Sylvester equation minimization problem under columnwise orthogonal constraints.Based on some geometric properties of the Stiefel manifold and the MPRP conjugate gradient method in Euclidean space,a Riemannian MPRP conjugate gradient algorithm with Armijo-type line search is proposed to solve the presented problem,and its global convergence is also established.An attractive property of the proposed method is that the direction generated by the method is always a descent direction for the objective function.Some numerical tests are given to show the efficiency of the proposed method.Comparisons with some existing methods are also given.

关 键 词：广义Sylvester方程 极小化问题 列正交约束 黎曼共轭梯度法 

分 类 号：O151.1[理学—数学]