Optimality Conditions in Set-valued Optimization Problem with Respect to a Partial Order Relation via Directional Derivative

Nonsmooth set variational inequality problems and optimality criteria for set optimization

“…Karaman et al [13] obtained some optimality conditions for (m − SVO P ) and existence theorems for M-directional derivative.…”

“…Naturally, it has been attracted the attention of scientists, who have been working in mathematics, engineering, economics, management, economic equilibria, optimal control, nonlinear optimization transportation, and many other disciplines. There are many methods to solve and obtain optimality conditions of the optimization problems such as scalarization [14], vectorization [10,12], directional derivative [13], subdifferential [9,11], embedding space [15,18], variational inequality problems [1, 2, 4-8, 19, 21].…”

“…The most important feature of these two order relations is a partial order relation on the family, which contains nonempty bounded sets of the space. These partial order relations are used in [11,[13][14][15] to obtain optimality criteria and solutions for set-valued optimization problems.…”

“…A new convexity concept called m-convexity, which is a generalization of known convexity in the literature, is given by using partial order relation. A relationship is obtained between m-convexity and M-directional derivative defined in [13].…”

Optimality Conditions of Interval-Valued Optimization Problems by Using Subdifferantials

“…Jahn [6] and Karaman et al [7] obtained some optimality conditions for set optimization by using vectorization. Jahn [8] and Karaman et al [9] studied on optimality conditions for set optimization by using directional derivative. Hernández and Rodríguez-Marín [10], Karaman et al [11] Chen and Jahn [12] obtained some results for set optimization and vector optimization by using subdifferential, respectively.…”