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Journal of Global Optimization

, Volume 68, Issue 3, pp 587–600 | Cite as

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

  • Abbas Sayadi-bander
  • Latif Pourkarimi
  • Refail Kasimbeyli
  • Hadi Basirzadeh
Article

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.

Keywords

Multiobjective optimization Efficiency \(\varepsilon \)-Efficiency Bishop and Phelps coradiant set Scalarization 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Abbas Sayadi-bander
    • 1
  • Latif Pourkarimi
    • 2
  • Refail Kasimbeyli
    • 3
  • Hadi Basirzadeh
    • 1
  1. 1.Department of Mathematics, Faculty of Mathematical Sciences and ComputerShahid Chamran University of AhvazAhvazIran
  2. 2.Department of MathematicsRazi UniversityKermanshahIran
  3. 3.Department of Industrial EngineeringAnadolu UniversityEskisehirTurkey

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