Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (2): 479-495.

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

Yueyuan Liu,Kai Wang,Shujuan Qin,Jiaofen Li*()   

  1. 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
  • Received:2020-03-26 Online:2021-04-26 Published:2021-04-29
  • Contact: Jiaofen Li E-mail:lixiaogui1290@163.com
  • Supported by:
    the NSFC(11761024);the NSFC(11561015);the NSFC(11961012);the GUET Excellent Graduate Thesis Program(2019YJSPY03);the GUET Graduate Innovation Project(2020YJSCX02);the NSF of Guangxi Province(2017GXNSFBA198082)

Abstract:

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.

Key words: Generalized Sylvester equation, Minimization problem, Columnwise orthogonal constraint, Riemannian conjugate gradient method

CLC Number: 

  • O151.1
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