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On the relations between different duals assigned to composed optimization problems

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  • Gert Wanka
  • Radu Boţ
  • Emese Vargyas

Abstract

For an optimization problem with a composed objective function and composed constraint functions we determine, by means of the conjugacy approach based on the perturbation theory, some dual problems to it. The relations between the optimal objective values of these duals are studied. Moreover, sufficient conditions are given in order to achieve equality between the optimal objective values of the duals and strong duality between the primal and the dual problems, respectively. Finally, some special cases of this problem are presented. Copyright Springer-Verlag 2007

Suggested Citation

  • Gert Wanka & Radu Boţ & Emese Vargyas, 2007. "On the relations between different duals assigned to composed optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 47-68, August.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:1:p:47-68
    DOI: 10.1007/s00186-007-0169-6
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    References listed on IDEAS

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    1. Wanka, Gert & Bot, Radu Ioan & Vargyas, Emese, 2007. "Duality for location problems with unbounded unit balls," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1252-1265, June.
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    Cited by:

    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.

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