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arXiv · 2401.10161

A Set-Valued Lagrange Theorem based on a Process for Convex Vector Programming

Fernando García-Castaño·M. A. Melguizo Padial
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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.

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Fernando García-Castaño, M. A. Melguizo Padial. 2024-01-15. A Set-Valued Lagrange Theorem based on a Process for Convex Vector Programming. https://doi.org/10.1080/02331934.2019.1616731

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