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


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.


Pointwise maximum Conjugate functions Attouch–Brézis regularity condition 

AMS Subject Classification

49N15 90C25 90C46 


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  1. 1.
    Attouch H. and Brézis H. (1986). Duality for the sum of convex functions in general Banach spaces. In: Barroso, J.A. (eds) Aspects of Mathematics and Its Applications, pp 125–133. North-Holland, Mathematical Library, Amsterdam Google Scholar
  2. 2.
    Boţ, R.I., Grad, S.M.: Regularity conditions for formulae of biconjugate functions (submitted)Google Scholar
  3. 3.
    Boţ R.I. and Wanka G. (2006). A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces. In: Nonlinear Anal. Theory Methods Appl. 64(12): 1367–1381 Google Scholar
  4. 4.
    Burachik R.S. and Jeyakumar V. (2005). A dual condition for the convex subdifferential sum formula with applications. J. Convex Anal. 12(2): 279–290 Google Scholar
  5. 5.
    Fitzpatrick S.P. and Simons S. (2000). On the pointwise maximum of convex functions. Proc. Am. Math. Soc. 128(12): 3553–3561 CrossRefGoogle Scholar
  6. 6.
    Zălinescu C. (1987). Solvability results for sublinear functions and operators. Zeitschrift für Operations Research 31: A79–A101 CrossRefGoogle Scholar
  7. 7.
    Zălinescu C. (2002). Convex analysis in general vector spaces. World Scientific, Singapore Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany

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