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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
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
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
Linking options:
https://www.mathnet.ru/eng/zvmmf10471 https://www.mathnet.ru/eng/zvmmf/v56/i10/p1733
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Abstract page: | 359 | Full-text PDF : | 36 | References: | 48 | First page: | 20 |
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