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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 10, Pages 1802–1811
(Mi zvmmf96)
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This article is cited in 3 scientific papers (total in 3 papers)
Two methods for minimizing convex functions in a class of nonconvex sets
Yu. A. Chernyaev Kazan State Technical University, ul. Karla Marksa 10, Kazan, 420111, Tatarstan, Russia
Abstract:
The conditional gradient method and the steepest descent method, which are conventionally used for solving convex programming problems, are extended to the case where the feasible set is the set-theoretic difference between a convex set and the union of several convex sets. Iterative algorithms are proposed, and their convergence is examined.
Key words:
$\varepsilon$-stationary point, conditional $\varepsilon$-subdifferential, necessary condition for a local minimum, minimization of convex functions.
Received: 26.10.2007
Citation:
Yu. A. Chernyaev, “Two methods for minimizing convex functions in a class of nonconvex sets”, Zh. Vychisl. Mat. Mat. Fiz., 48:10 (2008), 1802–1811; Comput. Math. Math. Phys., 48:10 (2008), 1768–1776
Linking options:
https://www.mathnet.ru/eng/zvmmf96 https://www.mathnet.ru/eng/zvmmf/v48/i10/p1802
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Statistics & downloads: |
Abstract page: | 320 | Full-text PDF : | 120 | References: | 38 | First page: | 7 |
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