Optimality and Duality for Invex Nonsmooth Multiobjective programming problems

Abstract

We consider nonsmooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions. Several sufficient optimality conditions under various (generalized) invexity assumptions and certain regularity conditions are presented. In addition, we introduce a Wolfe-type dual and Mond–Weir-type dual and establish duality relations under various (generalized) invexity and regularity conditions.

Keywords:

• Multiobjective programming
• Locally Lipschitz functions
• (generalized) Invexity
• Sufficient optimality conditions
• Duality relations
• Mathematics Subjects Classifications 2000: 90C29
• 49J52
• 49N15
• 90C46

Acknowledgements

This work was supported by the Korea Research Foundation Grant (KRF-2001-013-D00007). Professor Do Sang Kim gratefully acknowledges the support during his visit of the A.G. Anderson Graduate School of Management in 2002.