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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
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.
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
Linking options:
https://www.mathnet.ru/eng/zvmmf11125 https://www.mathnet.ru/eng/zvmmf/v60/i9/p1453
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Abstract page: | 125 | References: | 19 |
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