Characterizations On Henig Efficient Solutions And Benson Proper Efficient Solutions Of Set-valued Optimization Problem With Second-order Tangent Derivatives

In this thesis,a new type second-order tangent cone is proposed,and the relationship between it and other second-order tangent sets is discussed.With the cone,a new type second-order tangent derivative is defined and then the necessary optimality condition of set-valued optimization problem under Henig efficient solutions and Benson proper efficient solutions are investigated respectively.Examples are listed to demonstrate main conclusions.With second-order M-tangent derivatives,under the assumption of nearly cone-subconvexlikeness,by applying a separation theorem for convex sets,second-order Fritz John necessary optimality conditions is obtained for the Henig efficient solutions of set-valued optimization problem.Under the assumption of lower semicontinuity,a second-order Kuhn-Tucker sufficient optimality condition is obtained for the Henig efficient solutions of set-valued optimization problem.