Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold
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作者:
Oviedo, Harry
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Univ Adolfo Ibanez, Fac Ingn & Ciencias, Av Diag Torres 2640, Santiago 7941169, ChileUniv Adolfo Ibanez, Fac Ingn & Ciencias, Av Diag Torres 2640, Santiago 7941169, Chile
Oviedo, Harry
[1
]
机构:
[1] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Av Diag Torres 2640, Santiago 7941169, Chile
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.
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Texas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USATexas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USA
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Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Sha Tin, Hong Kong, Peoples R China
Chinese Univ Hong Kong, CUHK BGI Innovat Inst Trans, Sha Tin, Hong Kong, Peoples R ChinaTexas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USA
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Hong Kong Univ Sci & Technol, Clear Water Bay, Hong Kong, Peoples R ChinaTexas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USA
机构:
Texas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USATexas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USA
Chen, Shixiang
Ma, Shiqian
论文数: 0引用数: 0
h-index: 0
机构:
Univ Calif Davis, Dept Math, Davis, CA 95616 USATexas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USA
Ma, Shiqian
So, Anthony Man-Cho
论文数: 0引用数: 0
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Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Sha Tin, Hong Kong, Peoples R China
Chinese Univ Hong Kong, CUHK BGI Innovat Inst Trans, Sha Tin, Hong Kong, Peoples R ChinaTexas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USA
So, Anthony Man-Cho
Zhang, Tong
论文数: 0引用数: 0
h-index: 0
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Hong Kong Univ Sci & Technol, Clear Water Bay, Hong Kong, Peoples R ChinaTexas A&M Univ, Dept Ind & Syst Engn, College Stn, TX 77843 USA