A vectorization for nonconvex set-valued optimization
TURKISH JOURNAL OF MATHEMATICS, vol.42, no.4, pp.1815-1832, 2018 (SCI-Expanded, Scopus, TRDizin)
- 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
- Open Archive Collection: AVESIS Open Access Collection
- 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.