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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2018, Volume 24, Number 3, Pages 187–199
DOI: https://doi.org/10.21538/0134-4889-2018-24-3-187-199
(Mi timm1562)
 

This article is cited in 2 scientific papers (total in 2 papers)

The method of penalty functions and regularization in the analysis of improper convex programming problems

V. D. Skarinab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (232 kB) Citations (2)
References:
Abstract: We consider the questions of correction of improper convex programming problems, first of all, problems with inconsistent systems of constraints. Such problems often arise in the practice of mathematical simulation of specific applied settings in operations research. Since improper problems are rather frequent, it is important to develop methods of their correction, i.e., methods of construction of solvable models that are close to the original problems in a certain sense. Solutions of these models are taken as generalized (approximation) solutions of the original problems. We construct the correcting problems using a variation of the right-hand sides of the constraints with respect to the minimum of a certain penalty function, which, in particular, can be taken as some norm of the vector of constraints. As a result, we obtain optimal correction methods that are modifications of the (Tikhonov) regularized method of penalty functions. Special attention is paid to the application of the exact penalty method. Convergence conditions are formulated for the proposed methods and convergence rates are established.
Keywords: convex programming, improper problem, optimal correction, penalty function methods, Tikhonov regularization method.
Funding agency Grant number
Russian Science Foundation 14-11-00109
This work was supported by the Russian Science Foundation (project no. 14-11-00109).
Received: 17.05.2018
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2019, Volume 305, Issue 1, Pages S166–S177
DOI: https://doi.org/10.1134/S0081543819040175
Bibliographic databases:
Document Type: Article
UDC: 519.853
MSC: 47N05, 37N25, 37N40
Language: Russian
Citation: V. D. Skarin, “The method of penalty functions and regularization in the analysis of improper convex programming problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 3, 2018, 187–199; Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S166–S177
Citation in format AMSBIB
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\paper The method of penalty functions and regularization in the analysis of improper convex programming problems
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\vol 24
\issue 3
\pages 187--199
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\issue , suppl. 1
\pages S166--S177
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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