Second-order lower radial tangent derivatives and applications to set-valued optimization
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- 作者：Bihang Xu ; Zhenhua Peng ; Yihong Xu
- 关键词：Henig efficiency ; radial tangent derivative ; set ; valued optimization ; optimality condition
- 刊名：Journal of Inequalities and Applications
- 出版年：2017
- 出版时间：December 2017
- 年：2017
- 卷：2017
- 期：1
- 全文大小：1414KB
- 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
- 出版者：Springer International Publishing
- ISSN：1029-242X
- 卷排序：2017
文摘
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.