Karaman, E.2024-09-292024-09-2920201787-24051787-2413https://doi.org/10.18514/MMN.2020.3287https://hdl.handle.net/20.500.14619/6945In this work, set-valued optimization problems are considered according to an order relation, which is a partial order on the family such that contains nonempty bounded sets of the space. A generalized convexity is defined for set-valued mapping by using the partial order relation. Nonsmooth variational inequality problems are introduced with the aid of M-directionally derivative. Some optimality criteria including the necessary and sufficient optimality conditions are obtained for mentioned optimization problems.eninfo:eu-repo/semantics/openAccessset-valued optimizationvariational inequalitiesoptimality criteriaArticle10.18514/MMN.2020.32872-s2.0-850894682362401Q322921WOS:000541509200015Q2