A generalization of a theorem of Arrow, Barankin and Blackwell to a nonconvex case

Abstract

The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a partially ordered reflexive Banach space.

Keywords:

• Vector optimization
• density theorem
• nonlinear separation theorem
• augmented dual cone
• proper efficiency

AMS Subject Classifications:

• 90C26
• 90C29
• 90C30
• 90C46
• 46N10

Notes

No potential conflict of interest was reported by the authors.