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Tr. Mat. Inst. Steklova, 2007, Volume 256, Pages 6–30 (Mi tm453)  

This article is cited in 16 scientific papers (total in 16 papers)

Necessary Conditions for an Extremum in a Mathematical Programming Problem

E. R. Avakova, A. V. Arutyunovb, A. F. Izmailovc

a Institute of Control Sciences, Russian Academy of Sciences
b Peoples Friendship University of Russia
c M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: For minimization problems with equality and inequality constraints, first- and second-order necessary conditions for a local extremum are presented. These conditions apply when the constraints do not satisfy the traditional regularity assumptions. The approach is based on the concept of 2-regularity; it unites and generalizes the authors' previous studies based on this concept.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2007, 256, 2–25

Bibliographic databases:

UDC: 519.7
Received in July 2006

Citation: E. R. Avakov, A. V. Arutyunov, A. F. Izmailov, “Necessary Conditions for an Extremum in a Mathematical Programming Problem”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Tr. Mat. Inst. Steklova, 256, Nauka, MAIK Nauka/Inteperiodika, M., 2007, 6–30; Proc. Steklov Inst. Math., 256 (2007), 2–25

Citation in format AMSBIB
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\paper Necessary Conditions for an Extremum in a Mathematical Programming Problem
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\bookinfo Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov
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\vol 256
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\publ Nauka, MAIK Nauka/Inteperiodika
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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. 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
    2. Marinković B., “Optimality conditions for discrete optimal control problems with equality and inequality type of constraints”, Positivity, 12:3 (2008), 535–545  crossref  mathscinet  zmath  isi  elib  scopus
    3. Hernández-Jiménez B., Rojas-Medar M.A., Osuna-Gómez R., Beato-Moreno A., “Generalized convexity in non-regular programming problems with inequality-type constraints”, J. Math. Anal. Appl., 352:2 (2009), 604–613  crossref  mathscinet  zmath  isi  elib  scopus
    4. Arutyunov A.V., Karamzin D.Y., Pereira F.L., “Necessary optimality conditions for problems with equality and inequality constraints: abnormal case”, J. Optim. Theory Appl., 140:3 (2009), 391–408  crossref  mathscinet  zmath  isi  elib  scopus
    5. Tret'yakov A.A., “pth Order Kuhn-Tucker-Type Optimality Conditions for a Singular Inequality Constrained Optimization Problem”, Dokl. Math., 82:2 (2010), 780–783  crossref  mathscinet  zmath  isi  scopus
    6. Hernández-Jiménez B., Osuna-Gómez R., Arana-Jiménez M., Ruiz Garzón G., “Generalized convexity and efficiency for non-regular multiobjective programming problems with inequality-type constraints”, Nonlinear Anal., 73:8 (2010), 2463–2475  crossref  mathscinet  zmath  isi  elib  scopus
    7. Hernández-Jiménez B., Rojas-Medar M.A., Osuna-Gómez R., Rufián-Lizana A., “Characterization of weakly efficient solutions for non-regular multiobjective programming problems with inequality-type constraints”, J. Convex Anal., 18:3 (2011), 749–768  mathscinet  zmath  isi  elib
    8. 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
    9. Gfrerer H., “On Metric Pseudo-(Sub)Regularity of Multifunctions and Optimality Conditions for Degenerated Mathematical Programs”, Set-Valued Var. Anal., 22:1 (2014), 79–115  crossref  mathscinet  zmath  isi  scopus
    10. Tret'yakov A.A., Szczepanik E., “Irregular Optimization Models and P-Order Kuhn-Tucker Optimality Conditions”, J. Comput. Syst. Sci. Int., 53:3 (2014), 384–391  crossref  mathscinet  zmath  isi  scopus
    11. Toan N.T., Ansari Q.H., Yao J.-C., “Second-Order Necessary Optimality Conditions For a Discrete Optimal Control Problem”, J. Optim. Theory Appl., 165:3 (2015), 812–836  crossref  mathscinet  zmath  isi  elib  scopus
    12. Toan N.T., Thuy L.Q., “Second-order necessary optimality conditions for a discrete optimal control problem with mixed constraints”, J. Glob. Optim., 64:3, SI (2016), 533–562  crossref  mathscinet  zmath  isi  elib  scopus
    13. Le Quang Thuy, Bui Thi Thanh, Nguyen Thi Toan, “On the No-Gap Second-Order Optimality Conditions For a Discrete Optimal Control Problem With Mixed Constraints”, J. Optim. Theory Appl., 173:2 (2017), 421–442  crossref  mathscinet  zmath  isi  scopus
    14. Brezhneva O., Tret'yakov A.A., “When the Karush-Kuhn-Tucker Theorem Fails: Constraint Qualifications and Higher-Order Optimality Conditions For Degenerate Optimization Problems”, J. Optim. Theory Appl., 174:2 (2017), 367–387  crossref  mathscinet  zmath  isi  scopus
    15. Vivanco-Orellana V., Osuna-Gomez R., Hernandez-Jimenez B., Rojas-Medar M.A., “Optimality Conditions For Nonregular Optimal Control Problems and Duality”, Numer. Funct. Anal. Optim., 39:3 (2018), 361–382  crossref  mathscinet  zmath  isi  scopus
    16. Arutyunov A., Karamzin D., Pereira F.L., “a Remark on the Continuity of the Measure Lagrange Multiplier in State Constrained Optimal Control Problems”, 2018 IEEE Conference on Decision and Control (Cdc), IEEE Conference on Decision and Control, IEEE, 2018, 49–54  isi
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