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Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming

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Abstract

In a recent paper, Birgin, Floudas and Martínez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the \(\alpha \) BB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On the one hand, feasibility of the problem will not be required. Possible infeasibility will be detected in finite time by the new algorithms and optimal infeasibility results will be proved. On the other hand, finite termination results that guarantee optimality and/or feasibility up to any required precision will be provided. An adaptive modification in which subproblem tolerances depend on current feasibility and complementarity will also be given. The adaptive algorithm allows the augmented Lagrangian subproblems to be solved without requiring unnecessary potentially high precisions in the intermediate steps of the method, which improves the overall efficiency. Experiments showing how the new algorithms and results are related to practical computations will be given.

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Authors and Affiliations

  1. Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, SP, Brazil

    E. G. Birgin

  2. Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, SP, Brazil

    J. M. Martínez & L. F. Prudente

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  1. E. G. Birgin
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  2. J. M. Martínez
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  3. L. F. Prudente
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Correspondence to E. G. Birgin.

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This work was supported by PRONEX-CNPq/FAPERJ (E-26/111.449/2010-APQ1), FAPESP (2006/53768-0, 2009/10241-0, and 2010/10133-0) and CNPq (Grant 306802/2010-4).

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Birgin, E.G., Martínez, J.M. & Prudente, L.F. Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming. J Glob Optim 58, 207–242 (2014). https://doi.org/10.1007/s10898-013-0039-0

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