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Computational Optimization and Applications

, Volume 60, Issue 3, pp 609–631 | Cite as

Optimality properties of an Augmented Lagrangian method on infeasible problems

  • E. G. Birgin
  • J. M. Martínez
  • L. F. Prudente
Article

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.

Keywords

Nonlinear programming Infeasible domains Augmented Lagrangians Algorithms Numerical experiments 

Notes

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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • E. G. Birgin
    • 1
  • J. M. Martínez
    • 2
  • L. F. Prudente
    • 3
  1. 1.Department of Computer Science, Institute of Mathematics and StatisticsUniversity of São PauloSão PauloBrazil
  2. 2.Department of Applied Mathematics, Institute of Mathematics, Statistics, and Scientific ComputingUniversity of CampinasCampinasBrazil
  3. 3.Institute of Mathematics and StatisticsFederal University of GoiásGoiâniaBrazil

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