Optimality Conditions Of Set-valued Optimization With Ic-cone-convexlikeness

The set-valued optimization problem with constraints (SOP) is considered in thesense of strict efficiency in Hausdorff locally convex linear topological spaces.Given a property of the ic-cone-conevexlikeness, under the assumption of theic-cone-convexlikeness and condition (CQ), by applying alternative theorem,Kuhn-Tucker type, Lagrange type and Saddle points type optimality conditionsof vector set-valued optimization problem (SOP) are derived respectively.The subgadient, under the strict effciency, of a set-valued mapping is developed,the existence of the subgradient is proved, optimality conditions in terms ofLagrange multipliers for a strictly efficient point are established in the general caseand in the case with ic-cone-convexlike data.