Regularity Conditions and Optimality in Vector Optimization

Abstract

The aim of this article is to study necessary optimality conditions for a vector minimization program involving locally Lipschitz functions under certain general regularity conditions. We study problems involving only inequality and both inequality and equality constraints.

Key Words:

• Vector optimization
• Nonsmooth optimization
• Regularity conditions
• Convex optimization

Mathematical Subject Classification:

• Primary 90C29
• Secondary 90C46

Acknowledgment

The authors are grateful to Professor B. D. Craven his helpful comments which significantly improved an earlier version of the paper. The authors are thankful to Professor Pham Huu Sach for bringing reference (Dolezal, 1984) to our notice and very kindly providing a copy of the same. The authors are also grateful to Professor J. E. Martinez-Legaz who provided us a very simple counterexample to demonstrate that the Tucker Theorem of the Alternative fails for the convex case.