Abstract
In this article, the generalized radial epiderivative for a set-valued map is introduced. An existence result of generalized radial epiderivatives is obtained. Moreover, the relation between these kind of derivatives and radial epiderivatives has been established. Based on the generalized radial epiderivative, necessary and sufficient optimality conditions are derived for nonconvex set-valued optimization problems.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (11001287, 11171363), the Natural Science Foundation Project of Chongqing (CSTC 2010BB9254 and CSTC 2009BB8240), the Special Fund of Chongqing Key Laboratory (CSTC 2011KLORSE01) and the Education Committee Project Research Foundation of Chongqing (No. KJ100711).