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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 8, Pages 1363–1368 (Mi zvmmf424)  

This article is cited in 9 scientific papers (total in 9 papers)

Necessary optimality conditions in an abnormal optimization problem with equality constraints

A. V. Arutyunova, D. Yu. Karamzinb

a Department of Differential Equations, Russian University of Peoples' Friendship, ul. Miklukho-Maklaya 6, Moscow, 119198, Russia
b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: An abnormal minimization problem with equality constraints and a finite-dimensional image is examined. Second-order necessary conditions for this problem are given that strengthen previously known results.

Key words: abnormal optimization problem, second-order necessary optimality conditions.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:8, 1293–1298

Bibliographic databases:

UDC: 519.626
Received: 26.12.2005

Citation: A. V. Arutyunov, D. Yu. Karamzin, “Necessary optimality conditions in an abnormal optimization problem with equality constraints”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1363–1368; Comput. Math. Math. Phys., 46:8 (2006), 1293–1298

Citation in format AMSBIB
\by A.~V.~Arutyunov, D.~Yu.~Karamzin
\paper Necessary optimality conditions in an abnormal optimization problem with equality constraints
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 8
\pages 1363--1368
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 8
\pages 1293--1298

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    This publication is cited in the following articles:
    1. A. V. Arutyunov, D. Yu. Karamzin, “Necessary optimality conditions for abnormal problems with geometric constraints”, Comput. Math. Math. Phys., 47:3 (2007), 349–360  mathnet  crossref  mathscinet  zmath
    2. Arutyunov A.V., Izmailov A.F., Jacimovic V., “New bifurcation theorems via the second-order optimality conditions”, Journal of Mathematical Analysis and Applications, 359:2 (2009), 752–764  crossref  mathscinet  zmath  isi  scopus
    3. Arutyunov A.V., Karamzin D.Y., Pereira F.L., “Necessary Optimality Conditions for Problems with Equality and Inequality Constraints: Abnormal Case”, Journal of Optimization Theory and Applications, 140:3 (2009), 391–408  crossref  mathscinet  zmath  isi  scopus
    4. Jacimovic V., “Abstract Hopf bifurcation theorem and further extensions via second variation”, Nonlinear Analysis-Theory Methods & Applications, 73:8 (2010), 2426–2432  crossref  mathscinet  zmath  isi  scopus
    5. A. V. Arutyunov, D. Yu. Karamzin, “Regular zeros of quadratic maps and their application”, Sb. Math., 202:6 (2011), 783–806  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. A. V. Arutyunov, “Smooth abnormal problems in extremum theory and analysis”, Russian Math. Surveys, 67:3 (2012), 403–457  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Avakov E.R., Arutyunov A.V., Karamzin D.Yu., “On Second-Order Necessary Optimality Conditions in Finite-Dimensional Abnormal Optimization Problems”, Dokl. Math., 85:3 (2012), 328–330  crossref  mathscinet  zmath  isi  elib  elib  scopus
    8. Avakov E.R., Arutyunov A.V., Karamzin D.Yu., “Inverse function in the neighborhood of an abnormal point of a smooth map”, Dokl. Math., 85:3 (2012), 305–308  crossref  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    9. E. R. Avakov, A. V. Arutyunov, D. Yu. Karamzin, “An investigation of smooth maps in a neighbourhood of an abnormal point”, Izv. Math., 78:2 (2014), 213–250  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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