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This article is cited in 10 scientific papers (total in 10 papers)
An extension of the gradient projection method and Newton's method to extremum problems constrained by a smooth surface
Yu. A. Chernyaev Kazan Typolev National Research Technical University, ul. Karla Marksa 10, Kazan, 420111, Tatarstan, Russia
Abstract:
The gradient projection method and Newton’s method are extended to the case where the constraints are nonconvex and are represented by a smooth surface. Necessary extremum conditions and the convergence of the methods are examined.
Key words:
smooth surface, gradient projection method, Newton's method, projection on a nonconvex set, necessary condition for a local minimum, convergence of an algorithm.
Received: 22.04.2014 Revised: 17.12.2014
Citation:
Yu. A. Chernyaev, “An extension of the gradient projection method and Newton's method to extremum problems constrained by a smooth surface”, Zh. Vychisl. Mat. Mat. Fiz., 55:9 (2015), 1493–1502; Comput. Math. Math. Phys., 55:9 (2015), 1451–1460
Linking options:
https://www.mathnet.ru/eng/zvmmf10262 https://www.mathnet.ru/eng/zvmmf/v55/i9/p1493
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Abstract page: | 470 | Full-text PDF : | 184 | References: | 78 | First page: | 14 |
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