Yu. A. Chernyaev, “Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set”, Zh. Vychisl. Mat. Mat. Fiz., 56:10 (2016), 1733–1749; Comput. Math. Math. Phys., 56:10 (2016), 1716

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 10, Pages 1733–1749
DOI: https://doi.org/10.7868/S0044466916100057 (Mi zvmmf10471)

This article is cited in 7 scientific papers (total in 7 papers)

Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set

Yu. A. Chernyaev

Kazan National Research Technical University, Kazan, Tatarstan, Russia

Full-text PDF (275 kB) Citations (7)

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DOI: https://doi.org/10.7868/S0044466916100057

Abstract: The gradient projection method and Newton's method are generalized to the case of nonconvex constraint sets representing the set-theoretic intersection of a spherical surface with a convex closed set. Necessary extremum conditions are examined, and the convergence of the methods is analyzed.

Key words: spherical surface, convex closed set, gradient projection method, Newton's method, necessary conditions for a local minimum, convergence of an algorithm.

Received: 21.10.2015

English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 10, Pages 1716–1731
DOI: https://doi.org/10.1134/S0965542516100055

Bibliographic databases:

Document Type: Article

UDC: 519.658

Language: Russian

Citation: Yu. A. Chernyaev, “Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set”, Zh. Vychisl. Mat. Mat. Fiz., 56:10 (2016), 1733–1749; Comput. Math. Math. Phys., 56:10 (2016), 1716–1731

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This publication is cited in the following 7 articles:

Yu. A. Chernyaev, “Conditional gradient method for optimization problems with a constraint in the form of the intersection of a convex smooth surface and a convex compact set”, Comput. Math. Math. Phys., 63:7 (2023), 1191–1198
Yu. A. Chernyaev, “Gradient projection method for a class of optimization problems with a constraint in the form of a subset of points of a smooth surface”, Comput. Math. Math. Phys., 61:3 (2021), 368–375
V. I. Zabotin, P. A. Chernyshevsky, “Extension of Strongin's global optimization algorithm to a function continuous on a compact interval”, Kompyuternye issledovaniya i modelirovanie, 11:6 (2019), 1111–1119
Yu. A. Chernyaev, “Gradient projection method for optimization problems with a constraint in the form of the intersection of a smooth surface and a convex closed set”, Comput. Math. Math. Phys., 59:1 (2019), 34–45
V. I. Zabotin, Yu. A. Chernyaev, “Newton's method for minimizing a convex twice differentiable function on a preconvex set”, Comput. Math. Math. Phys., 58:3 (2018), 322–327
L. F. Petrov, “Search for periodic solutions of highly nonlinear dynamical systems”, Comput. Math. Math. Phys., 58:3 (2018), 384–393
Zh. Tang, J. Qin, J. Sun, B. Geng, “The gradient projection algorithm with adaptive mutation step length for non-probabilistic reliability index”, Teh. Vjesn., 24:1 (2017), 53–62

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

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Computational Mathematics and Mathematical Physics

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