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Reduction of Weak Exhausters and Optimality Conditions via Reduced Weak Exhausters

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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.

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Acknowledgments

The authors would like to thank the editor and anonymous referees for their kind and helpful remarks and comments. This study was supported by Anadolu University Scientific Research Projects Commission under the grant no 1201F018.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Anadolu University, 26470 , Eskişehir, Turkey

    Mahide Küçük, Yalçın Küçük, İlknur Atasever Güvenç & Didem Tozkan

  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614, Pozńan, Poland

    Ryszard Urbański & Jerzy Grzybowski

  3. Department of Mathematics, Faculty of Literature and Science, Uşak University, 64200, Uşak, Turkey

    Mustafa Soyertem

Authors
  1. Mahide Küçük
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  2. Ryszard Urbański
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  3. Jerzy Grzybowski
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  4. Yalçın Küçük
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  5. İlknur Atasever Güvenç
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  6. Didem Tozkan
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  7. Mustafa Soyertem
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Correspondence to Yalçın Küçük.

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Küçük, M., Urbański, R., Grzybowski, J. et al. Reduction of Weak Exhausters and Optimality Conditions via Reduced Weak Exhausters. J Optim Theory Appl 165, 693–707 (2015). https://doi.org/10.1007/s10957-014-0592-9

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  • DOI: https://doi.org/10.1007/s10957-014-0592-9

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