AN ALTERNATE GRADIENT METHOD FOR OPTIMIZATION PROBLEMS WITH ORTHOGONALITY CONSTRAINTS

被引：0

作者：

Sun, Yanmei ^{[1
]}

Huang, Yakui ^{[2
]}

机构：

[1] Hebei Univ Technol, Sch Sci, Tianjin 300401, Peoples R China

[2] Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2021年 / 11卷 / 04期

关键词：

Orthogonality constraint; Stiefel manifold; Alternate gradient method; Gradient projection; Gradient reflection; ALGORITHMS; MINIMIZATION; FRAMEWORK;

D O I：

10.3934/naco.2021003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a new alternate gradient (AG) method to solve a class of optimization problems with orthogonal constraints. In particular, our AG method alternately takes several gradient reflection steps followed by one gradient projection step. It is proved that any accumulation point of the iterations generated by the AG method satisfies the first-order optimal condition. Numerical experiments show that our method is efficient.

引用

页码：665 / 676

页数：12

共 21 条

[1] Steepest descent algorithms for optimization under unitary matrix constraint [J].

Abrudan, Traian E. ;

Eriksson, Jan ;

Koivunen, Visa .

IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2008, 56 (03) :1134-1147

[2]

Absil PA, 2008, OPTIMIZATION ALGORITHMS ON MATRIX MANIFOLDS, P1

[3] 2-POINT STEP SIZE GRADIENT METHODS [J].

BARZILAI, J ;

BORWEIN, JM .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1988, 8 (01) :141-148

[4] A direct formulation for sparse PCA using semidefinite programming [J].

d'Aspremont, Alexandre ;

El Ghaoui, Laurent ;

Jordan, Michael I. ;

Lanckriet, Gert R. G. .

SIAM REVIEW, 2007, 49 (03) :434-448

[5] Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming [J].

Dai, YH ;

Fletcher, R .

NUMERISCHE MATHEMATIK, 2005, 100 (01) :21-47

[6] The geometry of algorithms with orthogonality constraints [J].

Edelman, A ;

Arias, TA ;

Smith, ST .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1998, 20 (02) :303-353

[7] A procrustes problem on the Stiefel manifold [J].

Eldén, L ;

Park, H .

NUMERISCHE MATHEMATIK, 1999, 82 (04) :599-619

[8] A NEW FIRST-ORDER ALGORITHMIC FRAMEWORK FOR OPTIMIZATION PROBLEMS WITH ORTHOGONALITY CONSTRAINTS [J].

Gao, Bin ;

Liu, Xin ;

Chen, Xiaojun ;

Yuan, Ya-Xiang .

SIAM JOURNAL ON OPTIMIZATION, 2018, 28 (01) :302-332

[9] A note on semidefinite programming relaxations for polynomial optimization over a single sphere [J].

Hu Jiang ;

Jiang Bo ;

Liu Xin ;

Wen ZaiWen .

SCIENCE CHINA-MATHEMATICS, 2016, 59 (08) :1543-1560

[10] A framework of constraint preserving update schemes for optimization on Stiefel manifold [J].

Jiang, Bo ;

Dai, Yu-Hong .

MATHEMATICAL PROGRAMMING, 2015, 153 (02) :535-575

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