Some Concepts and Results from Convex Analysis

  • Sławomir Stańczak
  • Marcin Wiczanowski
  • Holger Boche
Chapter
Part of the Foundations in Signal Processing, Communications and Networking book series (SIGNAL, volume 3)

In this chapter, we collect definitions, notational conventions and several results from convex analysis that may be helpful in better understanding the material covered in this manuscript. Proofs are provided only for selected results concerning the notion of log-convexity and the convergence of gradient projection algorithms. For other proofs, the reader is referred to any standard analysis book (e.g., [39]) and [160, 162, 16].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sławomir Stańczak
    • 1
  • Marcin Wiczanowski
    • 1
  • Holger Boche
    • 2
  1. 1.Technische Universität Berlin Heinrich Hertz Chair for Mobile Communications and Fraunhofer German-Sino Lab for Mobile Communications10587 BerlinGermany
  2. 2.Technische Universität Berlin Heinrich Hertz Chair for Mobile Communications and Fraunhofer German-Sino Lab for Mobile Communications and Fraunhofer Institute for Telecommunications Heinrich Hertz Institute10587 BerlinGermany

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