Abstract
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.
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References
Zlobec, S.: Characterizing zero-derivative points. J. Glob. Optim. 46, 155–161 (2010). doi:10.1007/s10898-009-9457-4
Zlobec, S.: The fundamental theorem of calculus for Lipschitz functions. Math. Commun. 13, 215–232 (2008)
Zlobec, S.: Characterization of convexifiable functions. Optimization 55, 251–261 (2006)
Acknowledgements
This work was supported by the Croatian Science Foundation through research Grant IP-2016-06-6545.
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Jukić, D. An elementary proof of the quadratic envelope characterization of zero-derivative points. Optim Lett 12, 1155–1156 (2018). https://doi.org/10.1007/s11590-017-1174-1
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DOI: https://doi.org/10.1007/s11590-017-1174-1