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Minimisation Problems: General Theorems

  • Jean-Pierre Aubin
Part of the Graduate Texts in Mathematics book series (GTM, volume 140)

Abstract

The aim of this chapter is to show that a minimisation problem:
$$find\;\bar x \in K\;such\;that\;f\left( {\bar x} \right) \le f\left( x \right)\forall x \in K$$
has a solution when the set K is compact and the function f from K into ℝ is lower semi-continuous.

Keywords

Minimisation Problem Indicator Function General Theorem Unique Fixed Point Lower Semicontinuous 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-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jean-Pierre Aubin
    • 1
  1. 1.Réseau de Recherche Viabilité, Jeux, ContrôleParisFrance

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