![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
In this paper, generalized mth-order contingent epiderivative and generalized mth-order epiderivative of set-valued maps are introduced, respectively. By virtue of the generalized mth-order epiderivatives, generalized necessary and sufficient optimality conditions are obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a fixed set. Generalized Kuhn–Tucker type necessary and sufficient optimality conditions are also obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a set-valued map.
ACKNOWLEDGMENTS
The authors would like to thank the anonymous referees for their valuable comments and suggestions, which helped to improve the paper.
This research was partially supported by the National Natural Science Foundation of China (grant no. 10871216), Natural Science Foundation Project of CQ CSTC (grant no. 2008BB0346), and the Excellent Young Teachers Program of Chongqing Jiaotong University, China.
