Characterization of the Benson proper efficiency and scalarization in nonconvex vector optimization

Gasimov R.

MULTIPLE CRITERIA DECISION MAKING IN THE NEW MILLENNIUM, cilt.507, ss.189-198, 2001 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 507
  • Basım Tarihi: 2001
  • Dergi Adı: MULTIPLE CRITERIA DECISION MAKING IN THE NEW MILLENNIUM
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.189-198
  • Eskişehir Osmangazi Üniversitesi Adresli: Hayır

Özet

It is the aim of this paper to present some sufficient and necessary conditions for Benson properly efficient solutions of nonconvex optimization problems via scalarization. We consider a nonconvex vector optimization problem on a real normed space, partially ordered by a pointed convex cone with a closed bounded base. We introduce a class of convex cone-monotone functions and characterize the Benson properly efficient elements as minimal points of such functions. These characterizations are presented without any convexity, cone convexlikeness or cone boundedness assumptions on the vector optimization problem.