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Global minimization using an Augmented Lagrangian method with variable lower-level constraints

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Abstract

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the \({\varepsilon_{k}}\) -global minimization of the Augmented Lagrangian with simple constraints, where \({\varepsilon_k \to \varepsilon}\) . Global convergence to an \({\varepsilon}\) -global minimizer of the original problem is proved. The subproblems are solved using the αBB method. Numerical experiments are presented.

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Authors and Affiliations

  1. Department of Computer Science IME-USP, University of São Paulo, Rua do Matão 1010, Cidade Universitária, São Paulo, SP, 05508-090, Brazil

    E. G. Birgin

  2. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544, USA

    C. A. Floudas

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

    J. M. Martínez

Authors
  1. E. G. Birgin
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  2. C. A. Floudas
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  3. J. M. Martínez
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Correspondence to E. G. Birgin.

Additional information

E. G. Birgin was supported by PRONEX-Optimization PRONEX-CNPq/FAPERJ E-26/171.164/2003-APQ1), FAPESP (Grants 06/53768-0 and 06/51827-9) and CNPq (PROSUL 490333/2004-4). C. A. Floudas was supported by the National Science Foundation and the National Institute of Health (R01 GM52032). J. M. Martínez was supported by PRONEX-Optimization (PRONEX-CNPq/FAPERJ E-26/171.164/2003-APQ1), FAPESP (Grant 06/53768-0) and CNPq.

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Birgin, E.G., Floudas, C.A. & Martínez, J.M. Global minimization using an Augmented Lagrangian method with variable lower-level constraints. Math. Program. 125, 139–162 (2010). https://doi.org/10.1007/s10107-009-0264-y

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  • DOI: https://doi.org/10.1007/s10107-009-0264-y

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