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An inexact-restoration method for nonlinear bilevel programming problems

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Abstract

We present a new algorithm for solving bilevel programming problems without reformulating them as single-level nonlinear programming problems. This strategy allows one to take profit of the structure of the lower level optimization problems without using non-differentiable methods. The algorithm is based on the inexact-restoration technique. Under some assumptions on the problem we prove global convergence to feasible points that satisfy the approximate gradient projection (AGP) optimality condition. Computational experiments are presented that encourage the use of this method for general bilevel problems.

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Authors and Affiliations

  1. Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970, Campinas, SP, Brazil

    R. Andreani, A. Friedlander & S. A. Santos

  2. Faculdades Integradas Metropolitanas de Campinas-METROCAMP, Campinas, SP, Brazil

    S. L. C. Castro

  3. Banco Itaú and Universidade Presbiteriana Mackenzie, São Paulo, SP, Brazil

    J. L. Chela

Authors
  1. R. Andreani
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  2. S. L. C. Castro
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  3. J. L. Chela
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  4. A. Friedlander
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  5. S. A. Santos
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Corresponding author

Correspondence to A. Friedlander.

Additional information

This work was supported by PRONEX-Optimization (PRONEX—CNPq/FAPERJ E-26/171.164/2003—APQ1), FAPESP (Grants 06/53768-0 and 05-56773-1) and CNPq.

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Andreani, R., Castro, S.L.C., Chela, J.L. et al. An inexact-restoration method for nonlinear bilevel programming problems. Comput Optim Appl 43, 307–328 (2009). https://doi.org/10.1007/s10589-007-9147-4

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  • DOI: https://doi.org/10.1007/s10589-007-9147-4

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