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Zh. Vychisl. Mat. Mat. Fiz., 1985, Volume 25, Number 5, Pages 680–693 (Mi zvmmf4185)  

This article is cited in 21 scientific papers (total in 21 papers)

Conditions for an extremum for smooth problems with constraints of equality type

E. R. Avakov

Moscow

Full text: PDF file (1592 kB)

English version:
USSR Computational Mathematics and Mathematical Physics, 1985, 25:3, 24–32

Bibliographic databases:

UDC: 517.977.58
MSC: Primary 49K27; Secondary 46B99, 90C48
Received: 25.05.1984

Citation: E. R. Avakov, “Conditions for an extremum for smooth problems with constraints of equality type”, Zh. Vychisl. Mat. Mat. Fiz., 25:5 (1985), 680–693; U.S.S.R. Comput. Math. Math. Phys., 25:3 (1985), 24–32

Citation in format AMSBIB
\Bibitem{Ava85}
\by E.~R.~Avakov
\paper Conditions for an extremum for smooth problems with constraints of equality type
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1985
\vol 25
\issue 5
\pages 680--693
\mathnet{http://mi.mathnet.ru/zvmmf4185}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=796117}
\zmath{https://zbmath.org/?q=an:0571.49016}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1985
\vol 25
\issue 3
\pages 24--32
\crossref{https://doi.org/10.1016/0041-5553(85)90069-2}


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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. A. F. Izmailov, “Optimality conditions for degenerate extremum problems with inequality-type constraints”, Comput. Math. Math. Phys., 34:6 (1994), 723–736  mathnet  mathscinet  zmath  isi
    2. A. V. Arutyunov, “Second-order conditions in extremal problems with finite-dimensional range. 2-normal maps”, Izv. Math., 60:1 (1996), 39–65  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. F. Izmailov, “On Lagrange methods for finding degenerate solutions of constrained extremum problems”, Comput. Math. Math. Phys., 36:4 (1996), 423–429  mathnet  mathscinet  zmath  isi
    4. A. F. Izmailov, “Optimality conditions in extremal problems with nonregular inequality constraints”, Math. Notes, 66:1 (1999), 72–81  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. O. A. Brezhneva, A. A. Tret'yakov, A. Khmura, “Generalization of the concept of $p$-regularity and higher order optimality conditions”, Comput. Math. Math. Phys., 41:2 (2001), 187–196  mathnet  mathscinet  zmath  elib
    6. A. V. Arutyunov, A. F. Izmailov, “The sensitivity theory for abnormal optimization problems with equality constraints”, Comput. Math. Math. Phys., 43:2 (2003), 178–193  mathnet  mathscinet  zmath  elib
    7. Brezhneva O.A., Tret'yakov A.A., “Optimality conditions for degenerate extremum problems with equality constraints”, SIAM J Control Optim, 42:2 (2003), 729–745  crossref  mathscinet  zmath  isi
    8. E. R. Avakov, A. V. Arutyunov, “Inverse function theorem and conditions of extremum for abnormal problems with non-closed range”, Sb. Math., 196:9 (2005), 1251–1269  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. A. S. Matveev, “Theory of optimal control in the works of V. A. Yakubovich”, Autom. Remote Control, 67:10 (2006), 1645–1698  mathnet  crossref  mathscinet  zmath
    10. E. R. Avakov, A. V. Arutyunov, A. F. Izmailov, “Necessary Conditions for an Extremum in a Mathematical Programming Problem”, Proc. Steklov Inst. Math., 256 (2007), 2–25  mathnet  crossref  mathscinet  zmath  elib  elib
    11. E. R. Avakov, A. V. Arutyunov, A. F. Izmailov, “Exact penalties for optimization problems with 2-regular equality constraints”, Comput. Math. Math. Phys., 48:3 (2008), 346–353  mathnet  crossref  mathscinet  zmath  isi
    12. 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
    13. “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
    14. E. R. Avakov, G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Lagrange's principle in extremum problems with constraints”, Russian Math. Surveys, 68:3 (2013), 401–433  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. 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
    16. D. Yu. Karamzin, “The Dines theorem and some other properties of quadratic mappings”, Comput. Math. Math. Phys., 55:10 (2015), 1633–1641  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    17. E. R. Avakov, “Stability theorem and extremum conditions for abnormal problems”, Proc. Steklov Inst. Math., 291 (2015), 4–23  mathnet  crossref  crossref  isi  elib
    18. E. R. Avakov, V. G. Oleinikov, “Irregular trajectories in vakonomic mechanical systems”, Comput. Math. Math. Phys., 56:10 (2016), 1686–1694  mathnet  crossref  crossref  isi  elib
    19. Izmailov A.F., Kurennoy A.S., Solodov M.V., “Critical Solutions of Nonlinear Equations: Local Attraction For Newton-Type Methods”, Math. Program., 167:2 (2018), 355–379  crossref  isi
    20. Izmailov A.F., Kurennoy A.S., Solodov M.V., “Critical Solutions of Nonlinear Equations: Stability Issues”, Math. Program., 168:1-2, SI (2018), 475–507  crossref  isi
    21. A. V. Arutyunov, “IInvestigation of the sets of real solutions of non-linear equations”, Izv. Math., 83:2 (2019), 199–213  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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