In the paper, we describe various applications of the closedness and duality theorems of  and . First, the strong separability of a polyhedron and a linear image of a convex set is characterized. Then,it is shown how stability conditions (known from the generalized Fenchel-Rockafellar duality theory) can be reformulated as closedness conditions. Finally, we present a generalized Lagrange duality theorem for Lagrange programs described with cone-convex/cone-polyhedral mappings.
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