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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 11, Pages 1814–1824
DOI: https://doi.org/10.31857/S004446692111003X (Mi zvmmf11315) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Optimal control

The gradient projection method with Аrmijo's step size on manifolds

M. V. Balashov, R. A. Kamalov

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 117997, Moscow, Russia
Citations (6)
DOI: https://doi.org/10.31857/S004446692111003X
Abstract: The problem of minimizing a function with a Lipschitz continuous gradient is considered on a proximally smooth subset that is a smooth manifold without boundary. The gradient projection method with Armijo's step size is discussed, and its linear convergence is proved. An exact constant of proximal smoothness is obtained for various matrix sets and manifolds.
Key words: proximal smoothness, gradient projection method, nonconvex optimization problem, Armijo step size, matrix manifolds.
Received: 23.10.2020
Revised: 23.10.2020
Accepted: 09.07.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 11, Pages 1776–1786
DOI: https://doi.org/10.1134/S0965542521110038
Bibliographic databases:
Document Type: Article
UDC: 519.853.6
Language: Russian
Citation: M. V. Balashov, R. A. Kamalov, “The gradient projection method with Аrmijo's step size on manifolds”, Zh. Vychisl. Mat. Mat. Fiz., 61:11 (2021), 1814–1824; Comput. Math. Math. Phys., 61:11 (2021), 1776–1786
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/zvmmf11315
  • https://www.mathnet.ru/eng/zvmmf/v61/i11/p1814
    • This publication is cited in the following 6 articles:
    1. Orizon Pereira Ferreira, Yingchao Gao, Sándor Zoltán Németh, Petra Renáta Rigó, “Gradient projection method on the sphere, complementarity problems and copositivity”, J Glob Optim, 2024  crossref
    2. M. V. Balashov, K. Z. Biglov, A. A. Tremba, “O nekotorykh zadachakh s mnogoznachnymi otobrazheniyami”, Avtomat. i telemekh., 2024, no. 5, 58–85  mathnet  crossref
    3. M. V. Balashov, K. Z. Biglov, A. A. Tremba, “On Some Problems with Multivalued Mappings”, ARC, 85:5 (2024), 491  crossref
    4. M. V. Balashov, K. Z. Biglov, A. A. Tremba, “On Some Problems with Multivalued Mappings”, Autom Remote Control, 85:5 (2024), 422  crossref
    5. Alessandro Lanza, Serena Morigi, Giuseppe Recupero, “Variational graph p-Laplacian eigendecomposition under p-orthogonality constraints”, Comput Optim Appl, 2024  crossref
    6. M. V. Balashov, “The Lezanski – Polyak – Lojasiewicz inequality and the convergence of the gradient projection algorithm”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 23:1 (2023), 4–10  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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