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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Volume 291, Pages 10–29
DOI: https://doi.org/10.1134/S0371968515040020 (Mi tm3672) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Stability theorem and extremum conditions for abnormal problems

E. R. Avakov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (263 kB) Citations (3)
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DOI: https://doi.org/10.1134/S0371968515040020
Abstract: We prove a generalized inverse function theorem in a neighborhood of a singular point of a mapping. As corollaries to this theorem, we obtain an inverse function theorem, an error bound theorem, and a tangent cone theorem that extend and strengthen the corresponding classical results in the irregular case. Using these corollaries, we establish necessary extremum conditions that are meaningful for abnormal problems.
Received: January 15, 2015
English version:
Proceedings of the Steklov Institute of Mathematics, 2015, Volume 291, Pages 4–23
DOI: https://doi.org/10.1134/S0081543815080027
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: E. R. Avakov, “Stability theorem and extremum conditions for abnormal problems”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 291, MAIK Nauka/Interperiodica, Moscow, 2015, 10–29; Proc. Steklov Inst. Math., 291 (2015), 4–23
Citation in format AMSBIB
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\paper Stability theorem and extremum conditions for abnormal problems
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\bookinfo Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin
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\yr 2015
\vol 291
\pages 10--29
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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