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Fenchel Duality

  • 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, in the First order sufficient condition (2.1.2), one benefit of convexity in optimization: critical points of convex functions are global minimizers. In this section we extend the types of functions we consider in two important ways:
  1. (i)

    We do not require f to be differentiable.

     
  2. (ii)

    We allow f to take the value + ∞.

     

Keywords

Convex Function Convex Cone Closed Convex Cone Polar Cone Slater Condition 
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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