Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1707-75
Keywords
Set-valued optimization, nonconvex optimization, vectorization, optimality conditions
First Page
1815
Last Page
1832
Recommended Citation
KARAMAN, E, GÜVENÇ, İ. A, SOYERTEM, M, TOZKAN, D, KÜÇÜK, M, & KÜÇÜK, Y (2018). A vectorization for nonconvex set-valued optimization. Turkish Journal of Mathematics 42 (4): 1815-1832. https://doi.org/10.3906/mat-1707-75
