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On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

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Abstract

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem.

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Authors and Affiliations

  1. Engenharia de Sistemas e Computação, COPPE-UFRJ, CP 68511, Rio de Janeiro-RJ, CEP 21941-972, Brazil

    Regina S. Burachik

  2. Department of Industrial Engineering, Osmangazi University, Bademlik, 26030, Eskişehir, Turkey

    Nergiz A. Ismayilova

  3. Department of Industrial Engineering, Osmangazi University, Bademlik, 26030, Eskişehir, Turkey

    Rafail N. Gasimov

  4. School of Mathematics and Statistics, University of South Australia, Mawson Lakes, S.A., 5095, Australia

    C. Yalçin. Kaya

Authors
  1. Regina S. Burachik
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  2. Rafail N. Gasimov
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  3. Nergiz A. Ismayilova
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  4. C. Yalçin. Kaya
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Corresponding author

Correspondence to Regina S. Burachik.

Additional information

*Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2.

Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.

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Burachik, R.S., Gasimov, R.N., Ismayilova, N.A. et al. On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*. J Glob Optim 34, 55–78 (2006). https://doi.org/10.1007/s10898-005-3270-5

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  • DOI: https://doi.org/10.1007/s10898-005-3270-5

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