Characterization of properly optimal elements with variable ordering structures

Abstract

In vector optimization with a variable ordering structure, the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications, it was started to develop a comprehensive theory for these vector optimization problems. Thereby, also notions of proper efficiency were generalized to variable ordering structures. In this paper, we study the relation between several types of proper optimality. We give scalarization results based on new functionals defined by elements from the dual cones which allow complete characterizations also in the nonconvex case.

Keywords:

• vector optimization
• variable ordering structure
• proper efficiency
• scalarization

AMS Subject Classifications:

• 90C29
• 90C30
• 90C48

Acknowledgements

The authors thank the two anonymous referees for their careful reading and their very helpful comments on earlier versions of this manuscript which helped to improved the manuscript much.

Notes

No potential conflict of interest was reported by the authors.