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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 12, Pages 34–50 (Mi ivm8757)  
This article is cited in 6 scientific papers (total in 6 papers)

Inhomogeneous convex approximations of nonsmooth functions

M. V. Dolgopolik

Chair of Mathematical Modeling of Control Systems, St.-Petersburg State University, St.-Petersburg, Russia
Full-text PDF (263 kB) Citations (6)
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Abstract: In this paper we introduce notions of inhomogeneous upper convex and lower concave approximations of the increment of a nonsmooth function defined in a normed space and study exhaustive families of these approximations. In terms of the introduced notions we establish optimality conditions for various constrained and unconstrained extremum problems.
Keywords: nonsmooth analysis, inhomogeneous upper convex approximation, inhomogeneous lower concave approximation, exhaustive family of approximations, coexhauster.
Received: 24.10.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 12, Pages 28–42
DOI: https://doi.org/10.3103/S1066369X12120043
Bibliographic databases:
Document Type: Article
UDC: 517.988
Language: Russian
Citation: M. V. Dolgopolik, “Inhomogeneous convex approximations of nonsmooth functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 12, 34–50; Russian Math. (Iz. VUZ), 56:12 (2012), 28–42
Citation in format AMSBIB
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\by M.~V.~Dolgopolik
\paper Inhomogeneous convex approximations of nonsmooth functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 12
\pages 34--50
\mathnet{http://mi.mathnet.ru/ivm8757}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3137108}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 12
\pages 28--42
\crossref{https://doi.org/10.3103/S1066369X12120043}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84872223648}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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