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Russian Mathematical Surveys, 2012, Volume 67, Issue 3, Pages 403–457
DOI: https://doi.org/10.1070/RM2012v067n03ABEH004793 (Mi rm9478) 		 
This article is cited in 38 scientific papers (total in 38 papers)

Smooth abnormal problems in extremum theory and analysis

A. V. Arutyunov

Peoples Friendship University of Russia
English version PDF (861 kB) Citations (38) Russian version article
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DOI: https://doi.org/10.1070/RM2012v067n03ABEH004793
Abstract: A survey is given of results related to the inverse function theorem and to necessary and sufficient first- and second-order conditions for extrema in smooth extremal problems with constraints. The main difference between the results here and the classical ones is that the former are valid and meaningful without a priori normality assumptions.
Bibliography: 48 titles.
Keywords: abnormal point, Lagrange principle, necessary and sufficient second-order conditions for an extremum, 2-regularity, inverse function theorem, 2-normality, quadratic map.
Received: 14.06.2011
Bibliographic databases:
Document Type: Article
UDC: 519.7
MSC: Primary 47J07, 49K27; Secondary 15A63
Language: English
Original paper language: Russian
Citation: A. V. Arutyunov, “Smooth abnormal problems in extremum theory and analysis”, Russian Math. Surveys, 67:3 (2012), 403–457
Citation in format AMSBIB
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\paper Smooth abnormal problems in~extremum theory and analysis
\jour Russian Math. Surveys
\yr 2012
\vol 67
\issue 3
\pages 403--457
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    • This publication is cited in the following 38 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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