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Characterization of Lipschitz Continuous Difference of Convex Functions

  • SI: Analysis, Optimization and Applications
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Abstract

We give a necessary and sufficient condition for a difference of convex (DC, for short) functions, defined on a normed space, to be Lipschitz continuous. Our criterion relies on the intersection of the ε-subdifferentials of the involved functions.

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Acknowledgements

The research of the first author has been supported by the CONICYT of Chile, Fondecyt No. 1110019 and ECOS-Conicyt No. C10E08, and by the MICINN of Spain, grant MTM2008-06695-C03-02. The research of the second author has been supported by the MICINN of Spain, Grant MTM2011-29064-C03-01. He is affiliated to MOVE (Markets, Organizations and Votes in Economics).

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Authors and Affiliations

  1. Centro de Modelamiento Matemático (CMM), Universidad de Chile, Avda Blanco Encalada 2120, Piso 7, Santiago, Chile

    A. Hantoute

  2. Departament d’Economia i d’Història Econòmica, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    J. E. Martínez-Legaz

Authors
  1. A. Hantoute
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  2. J. E. Martínez-Legaz
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Correspondence to J. E. Martínez-Legaz.

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Hantoute, A., Martínez-Legaz, J.E. Characterization of Lipschitz Continuous Difference of Convex Functions. J Optim Theory Appl 159, 673–680 (2013). https://doi.org/10.1007/s10957-013-0291-y

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  • DOI: https://doi.org/10.1007/s10957-013-0291-y

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