Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold

被引:2
作者
Oviedo, Harry [1 ]
机构
[1] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Av Diag Torres 2640, Santiago 7941169, Chile
关键词
proximal point method; Stiefel manifold; orthogonality constraint; Riemannian optimization; ALTERNATING LINEARIZED MINIMIZATION; RANK REDUCTION; OPTIMIZATION; FACTORIZATION; CONVERGENCE; NONCONVEX;
D O I
10.3390/math11112414
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we consider the problem of minimizing a continuously differentiable function on the Stiefel manifold. To solve this problem, we develop a geodesic-free proximal point algorithm equipped with Euclidean distance that does not require use of the Riemannian metric. The proposed method can be regarded as an iterative fixed-point method that repeatedly applies a proximal operator to an initial point. In addition, we establish the global convergence of the new approach without any restrictive assumption. Numerical experiments on linear eigenvalue problems and the minimization of sums of heterogeneous quadratic functions show that the developed algorithm is competitive with some procedures existing in the literature.
引用
收藏
页数:17
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共 40 条
  • [1] Absil PA, 2008, OPTIMIZATION ALGORITHMS ON MATRIX MANIFOLDS, P1
  • [2] A modified proximal point method for DC functions on Hadamard manifolds
    Almeida, Yldenilson Torres
    da Cruz Neto, Joao Xavier
    Oliveira, Paulo Roberto
    Souza, Joao Carlos de Oliveira
    [J]. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2020, 76 (03) : 649 - 673
  • [3] 2-POINT STEP SIZE GRADIENT METHODS
    BARZILAI, J
    BORWEIN, JM
    [J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 1988, 8 (01) : 141 - 148
  • [4] Iteration-Complexity of Gradient, Subgradient and Proximal Point Methods on Riemannian Manifolds
    Bento, Glaydston C.
    Ferreira, Orizon P.
    Melo, Jefferson G.
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2017, 173 (02) : 548 - 562
  • [5] Extrema of sums of heterogeneous quadratic forms
    Bolla, M
    Michaletzky, G
    Tusnady, G
    Ziermann, M
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 269 : 331 - 365
  • [6] Proximal alternating linearized minimization for nonconvex and nonsmooth problems
    Bolte, Jerome
    Sabach, Shoham
    Teboulle, Marc
    [J]. MATHEMATICAL PROGRAMMING, 2014, 146 (1-2) : 459 - 494
  • [7] PROXIMAL GRADIENT METHOD FOR NONSMOOTH OPTIMIZATION OVER THE STIEFEL MANIFOLD
    Chen, Shixiang
    Ma, Shiqian
    So, Anthony Man-Cho
    Zhang, Tong
    [J]. SIAM JOURNAL ON OPTIMIZATION, 2020, 30 (01) : 210 - 239
  • [8] Dreisigmeyer D., PREPRINT
  • [9] Proximal point algorithm on Riemannian manifolds
    Ferreira, OP
    Oliveira, PR
    [J]. OPTIMIZATION, 2002, 51 (02) : 257 - 270
  • [10] SHIFTED CHOLESKY QR FOR COMPUTING THE QR FACTORIZATION OF ILL-CONDITIONED MATRICES
    Fukaya, Takeshi
    Kannan, Ramaseshan
    Nakatsukasa, Yuji
    Yamamoto, Yusaku
    Yanagisawa, Yuka
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2020, 42 (01) : A477 - A503