In this study, a new directional derivative is defined by using Minkowski difference. Some properties and existence theorems of this directional derivative are given. Moreover, necessary and sufficient optimality conditions are presented for set-valued optimization problems with respect to $m_1$ order relation via directional derivative.
"Optimality Conditions in Set-valued Optimization Problem with Respect to a Partial Order Relation via Directional Derivative." Taiwanese J. Math. 24 (3) 709 - 722, June, 2020. https://doi.org/10.11650/tjm/190604