Minimisation Problems: General Theorems

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


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.


Minimisation Problem Indicator Function General Theorem Unique Fixed Point Lower Semicontinuous Function 
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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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