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Journal of Global Optimization

, Volume 41, Issue 4, pp 625–632 | Cite as

The conjugate of the pointwise maximum of two convex functions revisited

  • Radu Ioan Boţ
  • Gert Wanka
Article

Abstract

In this paper we use the tools of the convex analysis in order to give a suitable characterization for the epigraph of the conjugate of the pointwise maximum of two proper, convex and lower semicontinuous functions in a normed space. By using this characterization we obtain, as a natural consequence, the formula for the biconjugate of the pointwise maximum of two functions, provided the so-called Attouch–Brézis regularity condition holds.

Keywords

Pointwise maximum Conjugate functions Attouch–Brézis regularity condition 

AMS Subject Classification

49N15 90C25 90C46 

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References

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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany

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