Super efficient solutions for set-valued maps

Abstract

Some properties for K-preinvex set-valued maps in terms of normal subdifferential are obtained. Furthermore, some sufficient conditions for existence of super minimal points and necessary optimality conditions for a general kind of super efficiency are established.

Keywords:

• set-valued maps
• K-preinvex functions
• normal subdifferential
• set-valued optimization
• super minimizers

AMS Subject Classifications::

• 26E25
• 26B25
• 90C29
• 49J52

Acknowledgements

The authors are grateful to the referee for valuable comments and remarks. The second author is partially supported by the Center of Excellence of Mathematics of University of Isfahan.