Hahn-Banach-type theorems and Subdifferentials for invariant and equivariant order continuous vector lattice-valued operators with applications to Optimization

Abstract

We give some versions of Hahn-Banach, sandwich, duality, Mo-
reau-Rockafellar-type theorems, optimality conditions and a formula for the sub-
dierential of composite functions for order continuous vector lattice-valued oper-
ators, invariant or equivariant with respect to a xed group G of homomorphisms.
As applications to optimization problems with both convex and linear constraints,
we present some Farkas and Kuhn-Tucker-type results.