Convex Analysis

  • Jonathan M. Borwein
  • Adrian S. Lewis
Part of the CMS Books in Mathematics / Ouvrages de mathématiques de la SMC book series (CMSBM)


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.


Convex Function Lower Semicontinuous Convex Analysis Closed Convex Cone Lagrangian Duality 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Jonathan M. Borwein
    • 1
  • Adrian S. Lewis
    • 2
  1. 1.Centre for Experimental and Constructive Mathematics, Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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