Journal of Global Optimization

, Volume 63, Issue 2, pp 297–318 | Cite as

Augmented Lagrangian methods for nonlinear programming with possible infeasibility

  • M. L. N. Gonçalves
  • J. G. Melo
  • L. F. Prudente
Original Paper


In this paper, we consider a nonlinear programming problem for which the constraint set may be infeasible. We propose an algorithm based on a large family of augmented Lagrangian functions and analyze its global convergence properties taking into account the possible infeasibility of the problem. We show that, in a finite number of iterations, the algorithm stops detecting the infeasibility of the problem or finds an approximate feasible/optimal solution with any required precision. We illustrate, by means of numerical experiments, that our algorithm is reliable for different Lagrangian/penalty functions proposed in the literature.


Global optimization Augmented Lagrangians Nonlinear programming Infeasibility 



This work was supported in part by Projeto 136/11- CAPES/MES-Cuba, CNPq Grant 471815/2012-8 and 444134/2014-0, and FAPEG/GO.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • M. L. N. Gonçalves
    • 1
  • J. G. Melo
    • 1
  • L. F. Prudente
    • 1
  1. 1.Institute of Mathematics and Statistics, Federal University of GoiasGoiâniaBrazil

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