Two Kinds Of Second-order Composed Tangent Derivatives And Its Applications

Y-tangent cone is introduced,whose relationship to the contingent cone is discussed.With which a new kind of second-order tangent derivatives,termed second-order composed tangent derivatives,is introduced,its relationship to other second-order composed tangent derivatives is discussed.Then,with the help of second-order composed tangent derivatives,optimality necessary conditions are established respectively for a Henig efficient solution and a globally proper efficient solution of set-valued optimization.A kind of second-order tangent derivatives is introduced,a second-order composed tangent derivative,for a set-valued function is introduced with help of radial tangent cone and contingent cone or Y-tangent cone,its relationship to other second-order composed tangent derivatives is discussed.by using those concept,optimality necessary conditions are established respectively for a Henig efficient solution?weak efficient solution?Benson efficient solution and f-efficient solution of set-valued optimization,some examples are given to illustrate those.