Hahn-Banach, Sandwich and Separation Theorems for Invariant Functionals with Values in Ordered Vector Spaces and Applications to Nonlinear Vector Programming

A. Boccuto
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A. Boccuto: Dipartimento di Matematica e Informatica, University of Perugia, via Vanvitelli 1, I-06123 Perugia, Italy

Academic Journal of Applied Mathematical Sciences, 2016, vol. 2, issue 6, 45-50

Abstract: We give a direct proof of Hahn-Banach and sandwich-type theorems in the setting of convex subinvariant functionals, and a result of separation of convex sets by means of an invariant affine manifold. As consequences and applications, we give some conditions for an optimal solution of minimization problems, proving a Farkas and a Kuhn-Tucker-type theorem.

Keywords: Partially ordered vector space; Amenability; Hahn-Banach theorem; Sandwich theorem; Farkas theorem; Kuhn-Tucker theorem. (search for similar items in EconPapers)
Date: 2016
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