Generalized radial epiderivatives and nonconvex set-valued optimization problems

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.

Keywords:

• nonconvex set-valued optimization problem
• generalized radial epiderivative
• weakly efficient solution
• Benson proper efficient solution
• radial cone
• optimality condition

AMS Subject Classifications::

• 90C26
• 90C46
• 49J52

View correction statement:

Generalized radial epiderivatives and 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).