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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 9, Pages 1453–1461
DOI: https://doi.org/10.31857/S0044466920090070 (Mi zvmmf11125) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Gradient projection method on matrix manifolds

M. V. Balashov

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia
Citations (5)
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DOI: https://doi.org/10.31857/S0044466920090070
Abstract: The minimization of a function with a Lipschitz continuous gradient on a proximally smooth subset of a finite-dimensional Euclidean space is considered. Under the restricted secant inequality, the gradient projection method as applied to the problem converges linearly. In certain cases, the linear convergence of the gradient projection method is proved for the real Stiefel or Grassmann manifolds.
Key words: Lipschitz continuous gradient, proximal smoothness, gradient projection method, metric projection, nonconvex optimization problem, restricted secant inequality, Stiefel manifold, Grassmann manifold.
Funding agency Grant number
Russian Science Foundation 16-11-10015
This work was supported by the Russian Science Foundation, project no. 16-11-10015.
Received: 26.11.2019
Revised: 24.12.2019
Accepted: 09.04.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 9, Pages 1403–1411
DOI: https://doi.org/10.1134/S0965542520090079
Bibliographic databases:
Document Type: Article
UDC: 519.853.6
Language: Russian
Citation: M. V. Balashov, “Gradient projection method on matrix manifolds”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1453–1461; Comput. Math. Math. Phys., 60:9 (2020), 1403–1411
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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