Scalar characterizations of cone-continuous set-valued maps

Abstract

In this paper we characterize the cone-continuous set-valued maps in terms of the semicontinuity of certain extended real-valued functions, defined by means of the polar cone, some new Gerstewitz-like scalarization functions, or by some new nonlinear scalarization functions based on the point-to-set distance.

Keywords:

• Set-valued maps
• cone-convexity
• cone-continuity
• scalarization functions
• polar cone
• point-to-set distance

AMS Subject Classifications:

• 54C60
• 58C07
• 26A15

Acknowledgements

We would like to express our gratitude to the anonymous referees for their helpful comments on the first version of this paper.

Notes

No potential conflict of interest was reported by the authors.