On some Fermat rules for set-valued optimization problems

Abstract

The aim of this article is to obtain necessary optimality conditions for Pareto minima in set-valued optimization problems. We employ a new method to derive generalized Fermat rules for set-valued optimization. This method is based on openness results for multifunctions and allows recovery of a large number of results and, at the same time, getting several new ones.

Keywords:

• set-valued mappings
• openness
• Fréchet coderivative
• Mordukhovich coderivative
• generalized Fermat rules

AMS Subject Classifications:

• 90C29
• 90C26
• 49J52

Acknowledgements

The authors thank one of the anonymous referees for his/her constructive remarks. This research was supported by the CNCSIS Grant Code ID 379/2007.