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Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming

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

Abstract

In a recent paper, Birgin, Floudas and Martínez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the $$\alpha $$ BB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On the one hand, feasibility of the problem will not be required. Possible infeasibility will be detected in finite time by the new algorithms and optimal infeasibility results will be proved. On the other hand, finite termination results that guarantee optimality and/or feasibility up to any required precision will be provided. An adaptive modification in which subproblem tolerances depend on current feasibility and complementarity will also be given. The adaptive algorithm allows the augmented Lagrangian subproblems to be solved without requiring unnecessary potentially high precisions in the intermediate steps of the method, which improves the overall efficiency. Experiments showing how the new algorithms and results are related to practical computations will be given. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • E. Birgin & J. Martínez & L. Prudente, 2014. "Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming," Journal of Global Optimization, Springer, vol. 58(2), pages 207-242, February.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:2:p:207-242
    DOI: 10.1007/s10898-013-0039-0
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    References listed on IDEAS

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    1. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    3. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    4. Emerson Castelani & André Martinez & J. Martínez & B. Svaiter, 2010. "Addressing the greediness phenomenon in Nonlinear Programming by means of Proximal Augmented Lagrangians," Computational Optimization and Applications, Springer, vol. 46(2), pages 229-245, June.
    5. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    6. Ernesto Birgin & J. Martínez, 2012. "Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization," Computational Optimization and Applications, Springer, vol. 51(3), pages 941-965, April.
    7. Ernesto G. Birgin & Emerson V. Castelani & André L. M. Martinez & J. M. Martínez, 2011. "Outer Trust-Region Method for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 142-155, July.
    8. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
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    Cited by:

    1. Nélida Echebest & María Daniela Sánchez & María Laura Schuverdt, 2016. "Convergence Results of an Augmented Lagrangian Method Using the Exponential Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 92-108, January.
    2. E. G. Birgin & J. M. Martínez, 2016. "On the application of an Augmented Lagrangian algorithm to some portfolio problems," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(1), pages 79-92, February.
    3. 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.

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