A vectorization for nonconvex set-valued optimization

Karaman E., Güvenç I. A., SOYERTEM M., Tozkan D., Küçük M., Küçük Y.

Turkish Journal of Mathematics, vol.42, no.4, pp.1815-1832, 2018 (SCI-Expanded, Scopus, TRDizin) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1707-75
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1815-1832
  • Keywords: Nonconvex optimization, Optimality conditions, Set-valued optimization, Vectorization
  • Uşak University Affiliated: Yes

Abstract

Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation. Some properties of this function are studied. Moreover, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption.