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Reduction of Weak Exhausters and Optimality Conditions via Reduced Weak Exhausters

Author

Listed:
  • Mahide Küçük

    (Anadolu University)

  • Ryszard Urbański

    (Adam Mickiewicz University)

  • Jerzy Grzybowski

    (Adam Mickiewicz University)

  • Yalçın Küçük

    (Anadolu University)

  • İlknur Atasever Güvenç

    (Anadolu University)

  • Didem Tozkan

    (Anadolu University)

  • Mustafa Soyertem

    (Uşak University)

Abstract

In this work, it is proved that weak exhausters of a positively homogeneous function can be reduced if weak subdifferential/superdifferential can be represented as the sum of a subset of it and weak subdifferential of zero function. It is also shown that weak exhausters can be reduced if this subset is the set of minimal elements of weak subdifferential/superdifferential with respect to weak subdifferential of zero function. At the end, some optimality conditions are given using reduced weak exhausters.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:3:d:10.1007_s10957-014-0592-9
    DOI: 10.1007/s10957-014-0592-9
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    References listed on IDEAS

    as
    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. 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. Majid E. Abbasov, 2017. "Comparison Between Quasidifferentials and Exhausters," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 59-75, October.
    2. Majid E. Abbasov, 2019. "Geometric conditions of reduction of exhausters," Journal of Global Optimization, Springer, vol. 74(4), pages 737-751, August.
    3. 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.
    4. 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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