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On the E-Epigraph of an E-Convex Function

Author

Listed:
  • D. I. Duca

    (Babeş-Bolyai University)

  • L. Lupşa

    (Babeş-Bolyai University)

Abstract

In Ref 1, Yang shows that some of the results obtained in Ref. 2 on E-convex programming are incorrect, but does not prove that the results which make the connection between an E-convex function and its E-epigraph are incorrect. In this note, we show that the results obtained in Ref. 2 concerning the characterization of an E-convex function f in terms of its E-epigraph are incorrect. Afterward, some characterizations of E-convex functions using a different notion of epigraph are given.

Suggested Citation

  • D. I. Duca & L. Lupşa, 2006. "On the E-Epigraph of an E-Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 341-348, May.
    • Handle: RePEc:spr:joptap:v:129:y:2006:i:2:d:10.1007_s10957-006-9059-y
    DOI: 10.1007/s10957-006-9059-y
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    References listed on IDEAS

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    1. X. M. Yang, 2001. "On E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 699-704, June.
    2. E. A. Youness, 1999. "E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 439-450, August.
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    Cited by:

    1. Babli Kumari & Anurag Jayswal, 2018. "Some properties of geodesic E-preinvex function and geodesic semi E-preinvex function on Riemannian manifolds," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 807-822, November.
    2. Akhlad Iqbal & Shahid Ali & I. Ahmad, 2012. "On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 239-251, October.

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