We have already seen that linear functions are always continuous. More generally, a remarkable feature of convex functions on E is that they must be continuous on the interior of their domains. Part of the surprise is that an algebraic/geometric assumption (convexity) leads to a topological conclusion (continuity). It is this powerful fact that guarantees the usefulness of regularity conditions like Adom f ∩ cont g ≠ ∅ (3.3.9), which we studied in the previous section.
KeywordsConvex Function Lower Semicontinuous Convex Analysis Closed Convex Cone Lagrangian Duality
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