Optimization Letters

, Volume 8, Issue 1, pp 391–393 | Cite as

On Weierstrass extreme value theorem

Short Communication

Abstract

We show that suitable restatements of the classical Weierstrass extreme value theorem give necessary and sufficient conditions for the existence of a global minimum and of both a global minimum and a global maximum.

Keywords

Global optima Existence of optimal solutions 

Mathematics Subject Classification (2010)

Primary 49J27 Secondary 90C48 

References

  1. 1.
    Ioffe, A., Lucchetti, R.E.: Generic well-posedness in minimization problems. Abstr. Appl. Anal. 4, 343–360 (2005)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Willard, S.: General Topology. Addison-Wesley, Reading (1970)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Departament d’Economia i d’Història EconòmicaUniversitat Autònoma de BarcelonaBellaterraSpain

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