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Coradiant sets and \(\varepsilon \)-efficiency in multiobjective optimization

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Abstract

This paper studies \(\varepsilon \)-efficiency in multiobjective optimization by using the so-called coradiant sets. Motivated by the nonlinear separation property for cones, a similar separation property for coradiant sets is investigated. A new notion, called Bishop–Phelps coradiant set is introduced and some appropriate properties of this set are studied. This paper also introduces the notions of \(\varepsilon \)-dual and augmented \(\varepsilon \)-dual for Bishop and Phelps coradiant sets. Using these notions, some scalarization and characterization properties for \(\varepsilon \)-efficient and proper \(\varepsilon \)-efficient points are proposed.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Abbas Sayadi-bander & Hadi Basirzadeh

  2. Department of Mathematics, Razi University, Kermanshah, Iran

    Latif Pourkarimi

  3. Department of Industrial Engineering, Anadolu University, Iki Eylul Campus, 26555, Eskisehir, Turkey

    Refail Kasimbeyli

Authors
  1. Abbas Sayadi-bander
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  2. Latif Pourkarimi
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  3. Refail Kasimbeyli
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  4. Hadi Basirzadeh
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Correspondence to Latif Pourkarimi.

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Sayadi-bander, A., Pourkarimi, L., Kasimbeyli, R. et al. Coradiant sets and \(\varepsilon \)-efficiency in multiobjective optimization. J Glob Optim 68, 587–600 (2017). https://doi.org/10.1007/s10898-016-0495-4

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  • DOI: https://doi.org/10.1007/s10898-016-0495-4

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