Coradiant sets and -efficiency in multiobjective optimization

Sayadi-bander A., Pourkarimi L., KASIMBEYLİ R., Basirzadeh H.

JOURNAL OF GLOBAL OPTIMIZATION, vol.68, no.3, pp.587-600, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1007/s10898-016-0495-4
  • Journal Name: JOURNAL OF GLOBAL OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.587-600
  • Keywords: Multiobjective optimization, Efficiency, epsilon-Efficiency, Bishop and Phelps coradiant set, Scalarization, EPSILON-DUALITY THEOREM, SADDLE-POINT THEOREMS, APPROXIMATE SOLUTIONS
  • Anadolu University Affiliated: Yes

Abstract

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