Fenchel Duality

  • 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, 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 + ∞.



Convex Function Convex Cone Closed Convex Cone Polar Cone Slater Condition 
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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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