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Trudy Mat. Inst. Steklova, 2015, Volume 291, Pages 10–29 (Mi tm3672)  

This article is cited in 2 scientific papers (total in 2 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

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.

DOI: https://doi.org/10.1134/S0371968515040020

Full text: PDF file (263 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 291, 4–23

Bibliographic databases:

UDC: 517.9
Received: January 15, 2015

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
\Bibitem{Ava15}
\by E.~R.~Avakov
\paper Stability theorem and extremum conditions for abnormal problems
\inbook Optimal control
\bookinfo Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 291
\pages 10--29
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3672}
\crossref{https://doi.org/10.1134/S0371968515040020}
\elib{https://elibrary.ru/item.asp?id=24776658}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 291
\pages 4--23
\crossref{https://doi.org/10.1134/S0081543815080027}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957577995}


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  • https://doi.org/10.1134/S0371968515040020
  • http://mi.mathnet.ru/eng/tm/v291/p10

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dontchev A.L., “Bartle-Graves Theorem Revisited”, Set-Valued Var. Anal.  crossref  mathscinet  isi
    2. E. Avakov, “Local controllability for abnormal systems”, SIAM J. Control Optim., 57:2 (2019), 947–962  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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