HAHN-BANACH-TYPE THEOREMS AND APPLICATIONS TO OPTIMIZATION FOR PARTIALLY ORDERED VECTOR SPACE-VALUED INVARIANT OPERATORS.

We prove sandwich, Hahn-Banach, Fenchel duality theorems and a version of the Moreau-Rockafellar formula for invariant partially ordered vector space-valued operators. As consequences and applications, we give some versions of Farkas and Kuhn-Tucker-type optimization results and separation theorems, we prove the equivalence of these results and give a further application to Tarski-type theorems and probability measures defined on suitable product spaces. [ABSTRACT FROM AUTHOR]