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Sequential equality-constrained optimization for nonlinear programming

Author

Listed:
  • E. G. Birgin

    (University of São Paulo)

  • L. F. Bueno

    (Federal University of São Paulo)

  • J. M. Martínez

    (State University of Campinas)

Abstract

A novel idea is proposed for solving optimization problems with equality constraints and bounds on the variables. In the spirit of sequential quadratic programming and sequential linearly-constrained programming, the new proposed approach approximately solves, at each iteration, an equality-constrained optimization problem. The bound constraints are handled in outer iterations by means of an augmented Lagrangian scheme. Global convergence of the method follows from well-established nonlinear programming theories. Numerical experiments are presented.

Suggested Citation

  • E. G. Birgin & L. F. Bueno & J. M. Martínez, 2016. "Sequential equality-constrained optimization for nonlinear programming," Computational Optimization and Applications, Springer, vol. 65(3), pages 699-721, December.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:3:d:10.1007_s10589-016-9849-6
    DOI: 10.1007/s10589-016-9849-6
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    References listed on IDEAS

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    1. Elizabeth Karas & Elvio Pilotta & Ademir Ribeiro, 2009. "Numerical comparison of merit function with filter criterion in inexact restoration algorithms using hard-spheres problems," Computational Optimization and Applications, Springer, vol. 44(3), pages 427-441, December.
    2. Nahid Banihashemi & C. Yalçın Kaya, 2013. "Inexact Restoration for Euler Discretization of Box-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 726-760, March.
    3. 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.
    4. Andreas Fischer & Ana Friedlander, 2010. "A new line search inexact restoration approach for nonlinear programming," Computational Optimization and Applications, Springer, vol. 46(2), pages 333-346, June.
    5. Juliano Francisco & J. Martínez & Leandro Martínez & Feodor Pisnitchenko, 2011. "Inexact restoration method for minimization problems arising in electronic structure calculations," Computational Optimization and Applications, Springer, vol. 50(3), pages 555-590, December.
    6. L. F. Bueno & G. Haeser & J. M. Martínez, 2015. "A Flexible Inexact-Restoration Method for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 188-208, April.
    7. 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.
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    Cited by:

    1. 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.
    2. Luís Felipe Bueno & Gabriel Haeser & Luiz-Rafael Santos, 2020. "Towards an efficient augmented Lagrangian method for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 76(3), pages 767-800, July.
    3. 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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