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On the relations between different duals assigned to composed optimization problems

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Gert Wanka & Radu Ioan Boţ

  2. Institute of Mathematics and its Didactics, University of Flensburg, 24943, Flensburg, Germany

    Emese Vargyas

Authors
  1. Gert Wanka
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  2. Radu Ioan Boţ
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  3. Emese Vargyas
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Correspondence to Gert Wanka.

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Wanka, G., Boţ, R.I. & Vargyas, E. On the relations between different duals assigned to composed optimization problems. Math Meth Oper Res 66, 47–68 (2007). https://doi.org/10.1007/s00186-007-0169-6

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  • DOI: https://doi.org/10.1007/s00186-007-0169-6

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