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

Author

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  • A. Boccuto

    (Dipartimento di Matematica e Informatica, University of Perugia, via Vanvitelli 1, I-06123 Perugia, Italy)

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.

Suggested Citation

  • A. Boccuto, 2016. "Hahn-Banach, Sandwich and Separation Theorems for Invariant Functionals with Values in Ordered Vector Spaces and Applications to Nonlinear Vector Programming," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 2(6), pages 45-50, 06-2016.
    • Handle: RePEc:arp:ajoams:2016:p:45-50
    DOI: arpgweb.com/?ic=journal&journal=17&info=aims
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