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Optimality properties of an Augmented Lagrangian method on infeasible problems

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Abstract

Sometimes, the feasible set of an optimization problem that one aims to solve using a Nonlinear Programming algorithm is empty. In this case, two characteristics of the algorithm are desirable. On the one hand, the algorithm should converge to a minimizer of some infeasibility measure. On the other hand, one may wish to find a point with minimal infeasibility for which some optimality condition, with respect to the objective function, holds. Ideally, the algorithm should converge to a minimizer of the objective function subject to minimal infeasibility. In this paper the behavior of an Augmented Lagrangian algorithm with respect to those properties will be studied.

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Acknowledgments

This work was supported by PRONEX-CNPq/FAPERJ E-26/111.449/2010-APQ1, FAPESP 2010/10133-0, 2013/05475-7, and 2013/07375-0, Capes/MES-Cuba 226/2012, Capes/Procad NF 21/2009, and CNPq 474160/2013-0.

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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

  3. Institute of Mathematics and Statistics, Federal University of Goiás, Goiânia, GO, Brazil

    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 L. F. Prudente.

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Birgin, E.G., Martínez, J.M. & Prudente, L.F. Optimality properties of an Augmented Lagrangian method on infeasible problems. Comput Optim Appl 60, 609–631 (2015). https://doi.org/10.1007/s10589-014-9685-5

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