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Necessary and Sufficient Conditions for Strong Fenchel–Lagrange Duality via a Coupling Conjugation Scheme

Author

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  • M. D. Fajardo

    (University of Alicante)

  • J. Vidal

    (Chemnitz University of Technology)

Abstract

Given a general primal problem and its Fenchel–Lagrange dual one, which is obtained by using a conjugation scheme based on coupling functions and the perturbational approach, the aim in this work is to establish conditions under which strong duality can be guaranteed. To this purpose, even convexity and properness are a compulsory requirement over the involved functions in the primal problem. Furthermore, two closedness-type regularity conditions and a characterization for strong duality are derived.

Suggested Citation

  • M. D. Fajardo & J. Vidal, 2018. "Necessary and Sufficient Conditions for Strong Fenchel–Lagrange Duality via a Coupling Conjugation Scheme," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 57-73, January.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:1:d:10.1007_s10957-017-1209-x
    DOI: 10.1007/s10957-017-1209-x
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    References listed on IDEAS

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    1. Abdelmalek Aboussoror & Samir Adly, 2011. "A Fenchel–Lagrange Duality Approach for a Bilevel Programming Problem with Extremal-Value Function," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 254-268, May.
    2. M. Fajardo & J. Vicente-Pérez & M. Rodríguez, 2012. "Infimal convolution, c-subdifferentiability, and Fenchel duality in evenly convex optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 375-396, July.
    3. R. I. Boţ & S. M. Grad & G. Wanka, 2006. "Fenchel-Lagrange Duality Versus Geometric Duality in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 33-54, April.
    4. 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.
    5. María D. Fajardo & Margarita M. L. Rodríguez & José Vidal, 2016. "Lagrange Duality for Evenly Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 109-128, January.
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    Cited by:

    1. Elimhan N. Mahmudov, 2020. "Infimal Convolution and Duality in Problems with Third-Order Discrete and Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 781-809, March.

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