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Sbornik: Mathematics, 2021, Volume 212, Issue 6, Pages 782–809
DOI: https://doi.org/10.1070/SM9431 (Mi sm9431) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Characterization of solutions of strong-weak convex programming problems

S. I. Dudov, M. A. Osiptsev

Saratov State University, Saratov, Russia
English version PDF (630 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM9431
Abstract: Finite-dimensional problems of minimizing a strongly or weakly convex function on a strongly or weakly convex set are considered. Necessary and sufficient conditions for solutions of such problems are presented, which are based on estimates for the behaviour of the objective function on the feasible set taking account of the parameters of strong or weak convexity, as well as certain local features of the set and the function. The mathematical programming problem is considered separately for strongly and weakly convex functions. In addition, necessary conditions for a global and a local solution with differentiable objective function are found, in which a ‘strong’ stationarity condition is assumed to hold.
Bibliography: 33 titles.
Keywords: strongly and weakly convex sets and functions, subdifferential, Lagrangian function, radius of local minimum, strong stationarity condition.
Received: 24.04.2020 and 17.12.2020
Russian version:
Matematicheskii Sbornik, 2021, Volume 212, Number 6, Pages 43–72
DOI: https://doi.org/10.4213/sm9431
Bibliographic databases:
Document Type: Article
UDC: 519.85
MSC: 49K10, 90C25
Language: English
Original paper language: Russian
Citation: S. I. Dudov, M. A. Osiptsev, “Characterization of solutions of strong-weak convex programming problems”, Mat. Sb., 212:6 (2021), 43–72; Sb. Math., 212:6 (2021), 782–809
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Russian version PDF:105
    English version PDF:35
    Russian version HTML:108
    References:24
    First page:9
     
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