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Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications

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Abstract

We derive first- and second-order necessary optimality conditions for set-constrained optimization problems under the constraint qualification-type conditions significantly weaker than Robinson’s constraint qualification. Our development relies on the so-called 2-regularity concept, and unifies and extends the previous studies based on this concept. Specifically, in our setting constraints are given by an inclusion, with an arbitrary closed convex set on the right-hand side. Thus, for the second-order analysis, some curvature characterizations of this set near the reference point must be taken into account.

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Authors and Affiliations

  1. Peoples Friendship University, Miklukho-Maklaya Str. 6, 117198, Moscow, Russia

    A. V. Arutyunov

  2. Institute for Control Problems RAS, Profsoyuznaya Str. 65, 117806, Moscow, Russia

    E. R. Avakov

  3. Faculty of Computational Mathematics and Cybernetics, Department of Operations Research, Moscow State University, Leninskiye Gori, GSP-2, 119992, Moscow, Russia

    A. F. Izmailov

Authors
  1. A. V. Arutyunov
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  2. E. R. Avakov
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  3. A. F. Izmailov
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Correspondence to A. F. Izmailov.

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Arutyunov, A.V., Avakov, E.R. & Izmailov, A.F. Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications. Math. Program. 114, 37–68 (2008). https://doi.org/10.1007/s10107-006-0082-4

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  • DOI: https://doi.org/10.1007/s10107-006-0082-4

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