Lower Semicontinuous Convex Functions

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


The theory of convex functions is most powerful in the presence of lower semicontinuity. A key property of lower semicontinuous convex functions is the existence of a continuous affine minorant, which we establish in this chapter by projecting onto the epigraph of the function.


Convex Function Measure Space Shannon Entropy Real Hilbert Space Nonempty Closed Convex Subset 
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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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