Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure

Shahbeyk S., Soleimani-damaneh M., KASIMBEYLİ R.

JOURNAL OF GLOBAL OPTIMIZATION, vol.71, no.2, pp.383-405, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 71 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1007/s10898-018-0614-5
  • Journal Name: JOURNAL OF GLOBAL OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.383-405
  • Keywords: Vector optimization, Variable ordering structure (VOS), Properly nondominated solution, Super nondominated solution, Augmented dual cone, Linear scalarization, Variational analysis, APPROXIMATE SOLUTIONS, OPTIMAL ELEMENTS, DOMINATION STRUCTURES, CONE-CONVEXITY, EFFICIENCY, SCALARIZATION, RESPECT, THEOREM, MAXIMIZATION, EXISTENCE
  • Anadolu University Affiliated: Yes

Abstract

In this paper, we introduce Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure. We prove the connections between Benson properly nondominated, Hartley properly nondominated, and super nondominated solutions under appropriate assumptions. Moreover, we establish some necessary and sufficient conditions for newly-defined solutions invoking an augmented dual cone approach, the linear scalarization, and variational analysis tools. In addition to the theoretical results, various clarifying examples are given.