A new ABB theorem in normed vector spaces

Abstract

We extend the Arrow, Barankin and Blackwell (ABB) theorem for Henig efficient points for nonconvex sets in normed vector spaces. The novelty of our result is especially represented by the fact that we do not assume compactness of the set; in fact it can be an unbounded asymptotically compact set. Our result subsumes several generalizations of this important theorem.

Keywords:

• Maximal point
• Properly efficient point
• Henig efficient point
• Density results
• Asymptotic cone
• Asymptotically compact set
• Mathematics Subject Classifications 2000: 90C29
• 90C30
• 49J27

Acknowledgement

The authors thank the referee for his/her suggestions which improved the presentation of this paper.