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New second-order contingent epiderivatives and set-valued optimization problems

Research paper by Sheng-kun Zhu, Sheng-jie Li

Indexed on: 01 Oct '16Published on: 01 Oct '16Published in: Acta Mathematicae Applicatae Sinica, English Series



Abstract

In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.