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Fenchel’s Duality Theorem for Nearly Convex Functions

Author

Listed:
  • R. I. Boţ

    (Chemnitz University of Technology)

  • S. M. Grad

    (Chemnitz University of Technology)

  • G. Wanka

    (Chemnitz University of Technology)

Abstract

We present an extension of Fenchel’s duality theorem by weakening the convexity assumptions to near convexity. These weak hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension to closely convex functions is not possible under these hypotheses.

Suggested Citation

  • R. I. Boţ & S. M. Grad & G. Wanka, 2007. "Fenchel’s Duality Theorem for Nearly Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 509-515, March.
    • Handle: RePEc:spr:joptap:v:132:y:2007:i:3:d:10.1007_s10957-007-9234-9
    DOI: 10.1007/s10957-007-9234-9
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    References listed on IDEAS

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    1. R. I. Boţ & G. Kassay & G. Wanka, 2005. "Strong Duality for Generalized Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 127(1), pages 45-70, October.
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