Optimization Letters

, Volume 12, Issue 5, pp 1155–1156 | Cite as

An elementary proof of the quadratic envelope characterization of zero-derivative points

  • Dragan Jukić
Short Communication


This note presents a simple and self-contained proof of Zlobec’s theorem (J Glob Optim 46:155–161, 2010) on quadratic envelope characterization of zero-derivative points for smooth functions in several variables with a Lipschitz derivative. Our proof does not require any knowledge about convexifiable functions.


Zero-derivative point Quadratic envelope characterization of zero-derivative point 



This work was supported by the Croatian Science Foundation through research Grant IP-2016-06-6545.


  1. 1.
    Zlobec, S.: Characterizing zero-derivative points. J. Glob. Optim. 46, 155–161 (2010). doi: 10.1007/s10898-009-9457-4 MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Zlobec, S.: The fundamental theorem of calculus for Lipschitz functions. Math. Commun. 13, 215–232 (2008)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Zlobec, S.: Characterization of convexifiable functions. Optimization 55, 251–261 (2006)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsJ.J. Strossmayer University of OsijekOsijekCroatia

Personalised recommendations