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Emil ERNST(emil.ernstunivcezanne.fr) Abstract: Given x, a point of a convex subset C of an Euclidean space, the two following statements are proven to be equivalent: (i) any convex function f : C → R is upper semicontinuous at x, and (ii) C is polyhedral at x. In the particular setting of closed convex mappings and Fσ domains, we prove that any closed convex function f : C → R is continuous at x if and only if C is polyhedral at x. This provides a converse to the celebrated GaleKleeRockafellar theorem. Keywords: continuity of convex functions, closed convex functions, polyhedral points, conical points, GaleKleeRockafellar theorem, linearly accessible points Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: unpublished: AixMarseille Universités, december 2011 Download: [PDF] Entry Submitted: 12/15/2011 Modify/Update this entry  
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