Abstract
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 Adorn f∩ cont g≠∅ (3.3.9), which we studied in the previous section.
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© 2006 Springer Science+Business Media, Inc.
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(2006). Convex Analysis. In: Convex Analysis and Nonlinear Optimization. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-31256-9_4
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DOI: https://doi.org/10.1007/978-0-387-31256-9_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-29570-1
Online ISBN: 978-0-387-31256-9
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