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Izvestiya: Mathematics, 2014, Volume 78, Issue 2, Pages 213–250
DOI: https://doi.org/10.1070/IM2014v078n02ABEH002686 (Mi im7928) 		 
This article is cited in 5 scientific papers (total in 5 papers)

An investigation of smooth maps in a neighbourhood of an abnormal point

E. R. Avakova, A. V. Arutyunovbc, D. Yu. Karamzind

a Institute of Control Sciences, Russian Academy of Sciences, Moscow
b Peoples Friendship University of Russia
c M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
d Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
English version PDF (501 kB) Citations (5)
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DOI: https://doi.org/10.1070/IM2014v078n02ABEH002686
Abstract: We study the solubility of systems of non-linear equations in a neighbourhood of an abnormal point and prove inverse function theorems that guarantee the existence of solutions satisfying a linear-root estimate in the neighbourhood of the abnormal point. We also address the related issue of necessary conditions for an extremum at an abnormal point in a finite-dimensional constrained problem. We obtain second-order necessary optimality conditions that improve the known results.
Keywords: inverse function theorem, abnormal point, conditional extremum problem.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00427
12-01-33023
Received: 14.10.2011
Revised: 04.06.2013
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2014, Volume 78, Issue 2, Pages 3–42
DOI: https://doi.org/10.4213/im7928
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 26B10, 49K27
Language: English
Original paper language: Russian
Citation: E. R. Avakov, A. V. Arutyunov, D. Yu. Karamzin, “An investigation of smooth maps in a neighbourhood of an abnormal point”, Izv. RAN. Ser. Mat., 78:2 (2014), 3–42; Izv. Math., 78:2 (2014), 213–250
Citation in format AMSBIB
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\paper An investigation of smooth maps in a~neighbourhood of an abnormal point
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  • https://www.mathnet.ru/eng/im/v78/i2/p3
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:829
    Russian version PDF:194
    English version PDF:11
    References:98
    First page:75
     
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