ABSTRACT
In this paper, we present a new set-valued Lagrange multiplier theorem for constrained convex set-valued optimization problems. We introduce the novel concept of Lagrange process. This concept is a natural extension of the classical concept of Lagrange multiplier where the conventional notion of linear continuous operator is replaced by the concept of closed convex process, its set-valued analogue. The behaviour of this new Lagrange multiplier based on a process is shown to be particularly appropriate for some types of proper minimal points and, in general, when it has a bounded base.
Acknowledgments
We thank the referee for him/her suggestions which have helped us to improve the overall aspect of the manuscript.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Fernando García-Castaño http://orcid.org/0000-0002-8352-8235