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Optimality properties of an Augmented Lagrangian method on infeasible problems

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  • E. Birgin
  • J. Martínez
  • L. Prudente

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. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • E. Birgin & J. Martínez & L. Prudente, 2015. "Optimality properties of an Augmented Lagrangian method on infeasible problems," Computational Optimization and Applications, Springer, vol. 60(3), pages 609-631, April.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:3:p:609-631
    DOI: 10.1007/s10589-014-9685-5
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    References listed on IDEAS

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    1. Chungen Shen & Sven Leyffer & Roger Fletcher, 2012. "A nonmonotone filter method for nonlinear optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 583-607, July.
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    Cited by:

    1. E. G. Birgin & G. Haeser & A. Ramos, 2018. "Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points," Computational Optimization and Applications, Springer, vol. 69(1), pages 51-75, January.

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