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.
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Supported in part by the National Natural Science Foundation of China under Grant No. 11601437, 11526165 and 11571055, the Scientific Research Fund of Sichuan Provincial Science and Technology Department under Grant No. 2015JY0237, the Fundamental Research Funds for the Central Universities under Grant No. JBK160129.
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Zhu, Sk., Li, Sj. New second-order contingent epiderivatives and set-valued optimization problems. Acta Math. Appl. Sin. Engl. Ser. 32, 983–994 (2016). https://doi.org/10.1007/s10255-016-0619-0
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DOI: https://doi.org/10.1007/s10255-016-0619-0