Nonsmooth multiobjective programming and constraint qualifications

Abstract

We consider a nonsmooth multiobjective programming problem with inequality and set constraints. By using the notion of convexificator, we extend the Abadie constraint qualification, and derive the strong Kuhn-Tucker necessary optimality conditions. Some other constraint qualifications have been generalized and their interrelations are investigated.

Keywords:

• constraint qualification
• multiobjective optimization
• nonsmooth analysis
• necessary conditions

AMS Subject Classifications::

• 49J52
• 90C29
• 90C46

Acknowledgements

The second author was partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Iran.