Second-Order Optimality Conditions In Vector Set-Valued Optimization

In order to give the second-order optimality conditions of the set-valued vectoroptimization problems, we introduce a concept of second-order epiderivatives ofset-valued maps in this paper. By this concept, we present a few necessary andsufficient conditions for a weakly efficient solution points, a Henig efficient solutionpoints, a global efficient solution,an f-efficent solution, respectively, for theset-valued vector optimization problems without constraints (VOP), and a necessaryconditions for a Benson efficient solution; moreover. We also present a fewnecessary conditions for a weakly efficient solution, a Henig efficient solution, aglobal efficient solution, an f-efficient solution, respectively, for the vectorset-valued optimizaition problems with constraints(VSOP).