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Optimality properties of an Augmented Lagrangian method on infeasible problems

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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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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Keywords

  • Nonlinear programming
  • Infeasible domains
  • Augmented Lagrangians
  • Algorithms
  • Numerical experiments