A vectorization for nonconvex set-valued optimization

Authors

EMRAH KARAMAN
İLKNUR ATASEVER GÜVENÇ
MUSTAFA SOYERTEM
DİDEM TOZKAN
MAHİDE KÜÇÜK
YALÇIN KÜÇÜK

DOI

10.3906/mat-1707-75

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.

Keywords

Set-valued optimization, nonconvex optimization, vectorization, optimality conditions

First Page

1815

Last Page

1832

Recommended Citation

KARAMAN, EMRAH; GÜVENÇ, İLKNUR ATASEVER; SOYERTEM, MUSTAFA; TOZKAN, DİDEM; KÜÇÜK, MAHİDE; and KÜÇÜK, YALÇIN (2018) "A vectorization for nonconvex set-valued optimization," Turkish Journal of Mathematics: Vol. 42: No. 4, Article 21. https://doi.org/10.3906/mat-1707-75
Available at: https://journals.tubitak.gov.tr/math/vol42/iss4/21