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Optimization in Metric Spaces

  • Diethard Pallaschke
  • Stefan Rolewicz
Part of the Mathematics and Its Applications book series (MAIA, volume 388)

Abstract

Let (X, τ) be a topological space. We say that a real-valued function f (x) defined on X is lower semi-continuous at a point x0 if for every ε > 0 there is a neighbourhood U of the point x0 such that
$$f\left( x \right) \geqslant f\left( {{x_0}} \right) + \varepsilon $$
(2.1.1)

Keywords

Banach Space Normed Space Lipschitz Function Linear Class Outer Approximation 
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 1997

Authors and Affiliations

  • Diethard Pallaschke
    • 1
  • Stefan Rolewicz
    • 2
  1. 1.Institute for Statistics and Mathematical EconomicsUniversity of KarlsruheKarlsruheGermany
  2. 2.Institute of Mathematics of the Polish Academy of SciencesWarsawPoland

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