Second-order lower radial tangent derivatives and applications to set-valued optimization

作者：Xu, Bihang; Peng, Zhenhua; Xu, Yihong^*

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017, 2017(1): 7.

DOI：10.1186/s13660-016-1275-x

• Henig efficiency
• radial tangent derivative
• set-valued optimization
• optimality condition

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.

• 出版日期2017-1-4
• 单位南昌大学; 武汉大学