Optimization methods of set-valued maps

In this study, some methods for set-valued optimization problems are examined. Vectorization functions are given for set-valued optimization problems with respect to set less order relation by using Gerstewitz function. Set order relations are defined to compare sets. It is shown that depending on the corresponding cone, these order relations are partial orders on the family of nonempty, bounded sets. Scalarization methods are obtained for set optimization problems with respect to these order relations. Additionally, a directional derivative is defined for set-valued maps. Some properties of the directional derivative are examined and existence theorems are obtained. By using the directional derivative, necessary and sufficient optimality conditions are studied for set-valued optimization problems with respect to partial order relation defined in this study.