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.
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.