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.
"Hahn-Banach-type Theorems and Applications to Optimization for Partially Ordered Vector Space-Valued Invariant Operators." Real Anal. Exchange 44 (2) 333 - 368, 2019. https://doi.org/10.14321/realanalexch.44.2.0333