Basic Concepts and Problems of Multivalued Analysis

  • Bernd Luderer
  • Leonid Minchenko
  • Tatyana Satsura
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 66)

Abstract

In this chapter we describe the main concepts and problems of convex and nonsmooth analysis, which are required as background knowledge for the further treatment. Some of the reviewed results are classical and well-known, other are more specific. For simplicity, we suppose the underlying space X to be finite-dimensional, i.e., we consider X = R n . By we denote the scalar product of two vectors x* and x from X, while |x| is the Euclidean norm of the vector x. Finally, B denotes the open unit ball with centre at 0, i.e. B= {x∈X||x|<1}.

Keywords

Convex Function Support Function Directional Derivative Tangent Cone Lipschitz Continuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Bernd Luderer
    • 1
  • Leonid Minchenko
    • 2
  • Tatyana Satsura
    • 2
  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany
  2. 2.Byelorussian State University of Informatics & RadioelectronicsMinskByelorussia

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