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On the Existence of a Saddle Value

Author

Listed:
  • F. Bonenti

    (Università degli Studi di Brescia)

  • J. E. Martínez-Legaz

    (Universitat Autònoma de Barcelona)

Abstract

In this work, we achieve a complete characterization of the existence of a saddle value, for bifunctions which are convex, proper, and lower semi continuous in their first argument, by considering new suitably defined notions of special directions of recession. As special cases, we obtain some recent results of Lagrangian duality theory on zero duality gap for convex programs.

Suggested Citation

  • F. Bonenti & J. E. Martínez-Legaz, 2015. "On the Existence of a Saddle Value," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 785-792, June.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:3:d:10.1007_s10957-014-0665-9
    DOI: 10.1007/s10957-014-0665-9
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    References listed on IDEAS

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    1. Emil Ernst & Michel Volle, 2013. "Zero Duality Gap for Convex Programs: A Generalization of the Clark–Duffin Theorem," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 668-686, September.
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