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Strong Duality for Generalized Convex Optimization Problems

Author

Listed:
  • R. I. Boţ

    (Chemnitz University of Technology)

  • G. Kassay

    (Babeş – Bolyai University)

  • G. Wanka

    (Chemnitz University of Technology)

Abstract

In this paper, strong duality for nearly-convex optimization problems is established. Three kinds of conjugate dual problems are associated to the primal optimization problem: the Lagrange dual, Fenchel dual, and Fenchel-Lagrange dual problems. The main result shows that, under suitable conditions, the optimal objective values of these four problems coincide.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:127:y:2005:i:1:d:10.1007_s10957-005-6392-5
    DOI: 10.1007/s10957-005-6392-5
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    Citations

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    Cited by:

    1. C. R. Chen & S. J. Li, 2009. "Different Conjugate Dual Problems in Vector Optimization and Their Relations," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 443-461, March.
    2. Najafi, Arsalan & Homaee, Omid & Jasiński, Michał & Tsaousoglou, Georgios & Leonowicz, Zbigniew, 2023. "Integrating hydrogen technology into active distribution networks: The case of private hydrogen refueling stations," Energy, Elsevier, vol. 278(PB).
    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. 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.
    5. Yalçın Küçük & İlknur Atasever & Mahide Küçük, 2012. "Weak Fenchel and weak Fenchel-Lagrange conjugate duality for nonconvex scalar optimization problems," Journal of Global Optimization, Springer, vol. 54(4), pages 813-830, December.
    6. Kasina, Saamrat & Hobbs, Benjamin F., 2020. "The value of cooperation in interregional transmission planning: A noncooperative equilibrium model approach," European Journal of Operational Research, Elsevier, vol. 285(2), pages 740-752.
    7. Li, S.J. & Chen, C.R. & Wu, S.Y., 2009. "Conjugate dual problems in constrained set-valued optimization and applications," European Journal of Operational Research, Elsevier, vol. 196(1), pages 21-32, July.
    8. 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.
    9. R. I. Boţ & S. M. Grad & G. Wanka, 2007. "New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 241-255, November.

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