A vectorization for nonconvex set-valued optimization

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Karaman E., ATASEVER GÜVENÇ İ., SOYERTEM M., TOZKAN D., KÜÇÜK M., KÜÇÜK Y.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.4, pp.1815-1832, 2018 (SCI-Expanded) identifier 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: Set-valued optimization, nonconvex optimization, vectorization, optimality conditions, TOTAL ORDERING CONES, VECTOR OPTIMIZATION, CONJUGATE DUALITY, SCALARIZATION, MAPS, RESPECT
  • Anadolu 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.