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

Abbas Sayadi-bander (), Latif Pourkarimi (), Refail Kasimbeyli () and Hadi Basirzadeh ()
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Abbas Sayadi-bander: Shahid Chamran University of Ahvaz
Latif Pourkarimi: Razi University
Refail Kasimbeyli: Anadolu University
Hadi Basirzadeh: Shahid Chamran University of Ahvaz

Journal of Global Optimization, 2017, vol. 68, issue 3, No 5, 587-600

Abstract: 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.

Keywords: Multiobjective optimization; Efficiency; $$\varepsilon $$ ε -Efficiency; Bishop and Phelps coradiant set; Scalarization (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-016-0495-4

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