Lower Semicontinuous Convex Functions

Chapter
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

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.

Keywords

Entropy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations