NONSMOOTH SET VARIATIONAL INEQUALITY PROBLEMS AND OPTIMALITY CRITERIA FOR SET OPTIMIZATION

摘要

In 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.