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.
Set-valued optimization, nonconvex optimization, vectorization, optimality conditions
KARAMAN, EMRAH; GÜVENÇ, İLKNUR ATASEVER; SOYERTEM, MUSTAFA; TOZKAN, DİDEM; KÜÇÜK, MAHİDE; and KÜÇÜK, YALÇIN
"A vectorization for nonconvex set-valued optimization,"
Turkish Journal of Mathematics: Vol. 42:
4, Article 21.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss4/21