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Optimality conditions for an exhausterable function on an exhausterable set

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  • Majid E. Abbasov

    (St. Petersburg State University, SPbSU)

Abstract

Exhausters are families of convex compact sets that allow one to represent directional derivative of the studied function at a point in the form of InfMax or SupMin of linear functions. Functions for which such a representation is valid we call exhausterable. This class of functions is quite wide and contains many nonsmooth ones. The set of exhausterable function is also called exhausterable. In the present paper we describe optimality conditions for an exhausterable function on an exhausterable set. These conditions can be used for solving many nondifferentiable optimization problems. An example that illustrate obtained results is provided.

Suggested Citation

  • Majid E. Abbasov, 2020. "Optimality conditions for an exhausterable function on an exhausterable set," Journal of Global Optimization, Springer, vol. 76(1), pages 57-67, January.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:1:d:10.1007_s10898-019-00858-y
    DOI: 10.1007/s10898-019-00858-y
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    References listed on IDEAS

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    1. Mahide Küçük & Ryszard Urbański & Jerzy Grzybowski & Yalçın Küçük & İlknur Atasever Güvenç & Didem Tozkan & Mustafa Soyertem, 2015. "Reduction of Weak Exhausters and Optimality Conditions via Reduced Weak Exhausters," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 693-707, June.
    2. Zsolt Ugray & Leon Lasdon & John Plummer & Fred Glover & James Kelly & Rafael Martí, 2007. "Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 328-340, August.
    3. M. Abbasov & V. Demyanov, 2013. "Proper and adjoint exhausters in nonsmooth analysis: optimality conditions," Journal of Global Optimization, Springer, vol. 56(2), pages 569-585, June.
    4. Majid E. Abbasov, 2017. "Comparison Between Quasidifferentials and Exhausters," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 59-75, October.
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    Cited by:

    1. Didem Tozkan, 2022. "On reduction of exhausters via a support function representation," Journal of Global Optimization, Springer, vol. 82(1), pages 105-118, January.

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