We prove sandwich, Hahn-Banach, Fenchel duality theorems and a version of the Moreau-Rockafellar formula for invariant partially or- dered vector space-valued operators. As consequences and applications, we give some versions of Farkas and Kuhn-Tucker-type optimization re- sults and separation theorems, we prove the equivalence of these results and give a further application to Tarski-type theorems and probability measures dened on suitable product spaces.
HAHN-BANACH-TYPE THEOREMS AND APPLICATIONS TO OPTIMIZATION FOR PARTIALLY ORDERED VECTOR SPACE-VALUED INVARIANT OPERATORS
ANTONIO BOCCUTO
2019
Abstract
We prove sandwich, Hahn-Banach, Fenchel duality theorems and a version of the Moreau-Rockafellar formula for invariant partially or- dered vector space-valued operators. As consequences and applications, we give some versions of Farkas and Kuhn-Tucker-type optimization re- sults and separation theorems, we prove the equivalence of these results and give a further application to Tarski-type theorems and probability measures dened on suitable product spaces.File in questo prodotto:
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