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

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

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 291, 4–23

Bibliographic databases:

UDC: 517.9

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, Tr. 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 Tr. 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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000369344400002} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957577995} 

• http://mi.mathnet.ru/eng/tm3672
• 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
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Avakov E., “Local Controllability For Abnormal Systems”, SIAM J. Control Optim., 57:2 (2019), 947–962
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