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Duality for Closed Convex Functions and Evenly Convex Functions

Author

Listed:
  • M. Volle

    (Avignon University)

  • J. E. Martínez-Legaz

    (Universitat Autònoma de Barcelona)

  • J. Vicente-Pérez

    (University of New South Wales)

Abstract

We introduce two Moreau conjugacies for extended real-valued functions h on a separated locally convex space. In the first scheme, the biconjugate of h coincides with its closed convex hull, whereas, for the second scheme, the biconjugate of h is the evenly convex hull of h. In both cases, the biconjugate coincides with the supremum of the minorants of h that are either continuous affine or closed (respectively, open) halfspaces valley functions.

Suggested Citation

  • M. Volle & J. E. Martínez-Legaz & J. Vicente-Pérez, 2015. "Duality for Closed Convex Functions and Evenly Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 985-997, December.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-013-0395-4
    DOI: 10.1007/s10957-013-0395-4
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    References listed on IDEAS

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    1. Goberna, Miguel A. & Rodri'guez, Margarita M.L., 2006. "Analyzing linear systems containing strict inequalities via evenly convex hulls," European Journal of Operational Research, Elsevier, vol. 169(3), pages 1079-1095, March.
    2. Jean-Paul Penot & Michel Volle, 1990. "On Quasi-Convex Duality," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 597-625, November.
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