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

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.