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Geometric conditions of reduction of exhausters

Author

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  • Majid E. Abbasov

    (St. Petersburg State University (SPbSU))

Abstract

Exhausters are families of convex compact sets. They allow one to represent the principal part of the increment of a studied function in the form of minimax or maximin of linear functions. The calculus of exhausters was developed in the last decade. It gives formulas for building these families for a wide class of functions. There have been developed a number of optimality conditions that are described in terms of exhausters. This led to emergence of new optimizations algorithms. So exhausters became an effective tool in the study of nonsmooth functions. Since exhausters are not uniquely defined an important problems of their minimality and reduction arise. These problems were studied by researchers for decades. In this paper we propose new conditions for the verification of exhauster minimality and develop procedures for their reduction. The main advantage of our approach is its transparent geometric meaning.

Suggested Citation

  • Majid E. Abbasov, 2019. "Geometric conditions of reduction of exhausters," Journal of Global Optimization, Springer, vol. 74(4), pages 737-751, August.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:4:d:10.1007_s10898-018-0683-5
    DOI: 10.1007/s10898-018-0683-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Jerzy Grzybowski & Diethard Pallaschke & Ryszard Urbański, 2010. "Reduction of finite exhausters," Journal of Global Optimization, Springer, vol. 46(4), pages 589-601, April.
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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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