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Convex Analysis

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

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 Adom f ∩ cont g ≠ ∅ (3.3.9), which we studied in the previous section.

Keywords

Convex Function Lower Semicontinuous Convex Analysis Closed Convex Cone Lagrangian Duality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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