A Set-Valued Lagrange Theorem based on a Process for Convex Vector Programming
Optimization and Control
2024-01-19 v1
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.
Cite
@article{arxiv.2401.10161,
title = {A Set-Valued Lagrange Theorem based on a Process for Convex Vector Programming},
author = {Fernando García-Castaño and M. A. Melguizo Padial},
journal= {arXiv preprint arXiv:2401.10161},
year = {2024}
}