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Augmented Lagrangian methods for nonlinear programming with possible infeasibility

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  • M. Gonçalves
  • J. Melo
  • L. Prudente

Abstract

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. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • M. Gonçalves & J. Melo & L. Prudente, 2015. "Augmented Lagrangian methods for nonlinear programming with possible infeasibility," Journal of Global Optimization, Springer, vol. 63(2), pages 297-318, October.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:2:p:297-318
    DOI: 10.1007/s10898-015-0289-0
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    References listed on IDEAS

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    1. N. V. Sahinidis & I. E. Grossmann, 1992. "Reformulation of the Multiperiod MILP Model for Capacity Expansion of Chemical Processes," Operations Research, INFORMS, vol. 40(1-supplem), pages 127-144, February.
    2. R. Polyak & I. Griva, 2004. "Primal-Dual Nonlinear Rescaling Method for Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 111-156, July.
    3. Regina Burachik & Alfredo Iusem & Jefferson Melo, 2010. "A primal dual modified subgradient algorithm with sharp Lagrangian," Journal of Global Optimization, Springer, vol. 46(3), pages 347-361, March.
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    Cited by:

    1. M. Joseane F. G. Macêdo & Elizabeth W. Karas & M. Fernanda P. Costa & Ana Maria A. C. Rocha, 2020. "Filter-based stochastic algorithm for global optimization," Journal of Global Optimization, Springer, vol. 77(4), pages 777-805, August.
    2. Paul Armand & Ngoc Nguyen Tran, 2019. "An Augmented Lagrangian Method for Equality Constrained Optimization with Rapid Infeasibility Detection Capabilities," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 197-215, April.
    3. Chao Min & Feifei Fan & Zhaozhong Yang & Xiaogang Li, 2019. "An Iterative Algorithm for the Nonlinear MC 2 Model with Variational Inequality Method," Mathematics, MDPI, vol. 7(6), pages 1-13, June.

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