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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 9, Pages 1453–1461 (Mi zvmmf11125)  

This article is cited in 1 scientific paper (total in 1 paper)

Gradient projection method on matrix manifolds

M. V. Balashov

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia

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.


DOI: https://doi.org/10.31857/S0044466920090070


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:9, 1403–1411

Bibliographic databases:

UDC: 519.853.6
Received: 26.11.2019
Revised: 24.12.2019
Accepted:09.04.2020

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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\by M.~V.~Balashov
\paper Gradient projection method on matrix manifolds
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 9
\pages 1453--1461
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\crossref{https://doi.org/10.31857/S0044466920090070}
\elib{https://elibrary.ru/item.asp?id=43832505}
\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 9
\pages 1403--1411
\crossref{https://doi.org/10.1134/S0965542520090079}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85094647075}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Balashov, “On the Gradient Projection Method for Weakly Convex Functions on a Proximally Smooth Set”, Math. Notes, 108:5 (2020), 643–651  mathnet  crossref  crossref  mathscinet  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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