A set-valued Lagrange theorem based on a process for convex vector programming. (2nd November 2019)

• Record Type: Journal Article
• Authors: García-Castaño, Fernando; Melguizo Padial, M. A.
• Is Part Of: Optimization. Volume 68:Number 11(2019)
• Page Start: 2227
• Page End: 2245
• Publication Date: 2019-11-02
• Subjects: Lagrange multiplier -- convex vector optimization -- process -- optimality conditions; 90C29 -- 90C25 -- 90C31 -- 90C48; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1616731
• Languages: English
• ISSNs: 0233-1934

Abstract

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.