Duality in Convex Optimization

  • Heinz H. Bauschke
  • Patrick L. Combettes
Part of the CMS Books in Mathematics book series (CMSBM)


A convex optimization problem can be paired with a dual problem involving the conjugates of the functions appearing it its (primal) formulation. In this chapter, we study the interplay between primal and dual problems in the context of Fenchel–Rockafellar duality and, more generally, for bivariate functions. The latter approach leads naturally to saddle points and Lagrangians. Special attention is given to minimization under equality constraints and under inequality constraints. We start with a discussion of instances in which all primal solutions can be recovered from an arbitrary dual solution.


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics Irving K. Barber SchoolUniversity of British ColumbiaKelownaCanada
  2. 2.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie Curie - Paris 6ParisFrance

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