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Coradiant sets and $$\varepsilon $$ ε -efficiency in multiobjective optimization

Author

Listed:
  • Abbas Sayadi-bander

    (Shahid Chamran University of Ahvaz)

  • Latif Pourkarimi

    (Razi University)

  • Refail Kasimbeyli

    (Anadolu University)

  • Hadi Basirzadeh

    (Shahid Chamran University of Ahvaz)

Abstract

This paper studies $$\varepsilon $$ ε -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 $$\varepsilon $$ ε -dual and augmented $$\varepsilon $$ ε -dual for Bishop and Phelps coradiant sets. Using these notions, some scalarization and characterization properties for $$\varepsilon $$ ε -efficient and proper $$\varepsilon $$ ε -efficient points are proposed.

Suggested Citation

  • Abbas Sayadi-bander & Latif Pourkarimi & Refail Kasimbeyli & Hadi Basirzadeh, 2017. "Coradiant sets and $$\varepsilon $$ ε -efficiency in multiobjective optimization," Journal of Global Optimization, Springer, vol. 68(3), pages 587-600, July.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:3:d:10.1007_s10898-016-0495-4
    DOI: 10.1007/s10898-016-0495-4
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    References listed on IDEAS

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    8. C. Gutiérrez & B. Jiménez & V. Novo, 2006. "On Approximate Efficiency in Multiobjective Programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 165-185, August.
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    Cited by:

    1. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
    2. Refail Kasimbeyli & Masoud Karimi, 2021. "Duality in nonconvex vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 139-160, May.

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