title: Second-order lower radial tangent derivatives and applications to set-valued optimization.
abstract: We introduce the concepts of second-order radial composed tangent derivative, second-order radial tangent derivative, second-order lower radial composed tangent derivative, and second-order lower radial tangent derivative for set-valued maps by means of a radial tangent cone, second-order radial tangent set, lower radial tangent cone, and second-order lower radial tangent set, respectively. Some properties of second-order tangent derivatives are discussed, using which second-order necessary optimality conditions are established for a point pair to be a Henig efficient element of a set-valued optimization problem, and in the expressions the second-order tangent derivatives of the objective function and the constraint function are separated.
authors.affiliation: School of Information Engineering, Nanchang University, Nanchang, 330031 China.
authors.forename: Bihang
authors.initials: B
authors.lastname: Xu
authors.affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan, 430072 China ; Department of Mathematics, Nanchang University, Nanchang, 330031 China.
authors.forename: Zhenhua
authors.initials: Z
authors.lastname: Peng
authors.affiliation: Department of Mathematics, Nanchang University, Nanchang, 330031 China.
authors.forename: Yihong
authors.initials: Y
authors.lastname: Xu
keywords: Henig efficiency; optimality condition; radial tangent derivative; set-valued optimization