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Zero Duality Gap for Convex Programs: A Generalization of the Clark–Duffin Theorem

Author

Listed:
  • Emil Ernst

    (Aix-Marseille Université, UMR7353)

  • Michel Volle

    (Université d’Avignon et des Pays de Vaucluse)

Abstract

This article uses classical notions of convex analysis over Euclidean spaces, like Gale & Klee’s boundary rays and asymptotes of a convex set, or the inner aperture directions defined by Larman and Brøndsted for the same class of sets, to provide a generalization of the Clark–Duffin Theorem. On this ground, we are able to characterize objective functions and, respectively, feasible sets for which the duality gap is always zero, regardless of the value of the constraints and, respectively, of the objective function.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:3:d:10.1007_s10957-013-0287-7
    DOI: 10.1007/s10957-013-0287-7
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    Cited by:

    1. 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.
    2. Fabián Flores-Bazán & Filip Thiele, 2022. "On the Lower Semicontinuity of the Value Function and Existence of Solutions in Quasiconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 390-417, November.
    3. Gulcin Dinc Yalcin & Refail Kasimbeyli, 2020. "On weak conjugacy, augmented Lagrangians and duality in nonconvex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 199-228, August.

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