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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 10, Pages 1802–1811 (Mi zvmmf96)  
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
Full-text PDF (1375 kB) Citations (3)
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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
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 10, Pages 1768–1776
DOI: https://doi.org/10.1134/S0965542508100047
Bibliographic databases:
Document Type: Article
UDC: 519.658
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:38
    First page:7
     
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