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Outer Trust-Region Method for Constrained Optimization

Author

Listed:
  • Ernesto G. Birgin

    (University of São Paulo)

  • Emerson V. Castelani

    (University of Campinas)

  • André L. M. Martinez

    (University of Campinas)

  • J. M. Martínez

    (University of Campinas)

Abstract

Given an algorithm A for solving some mathematical problem based on the iterative solution of simpler subproblems, an outer trust-region (OTR) modification of A is the result of adding a trust-region constraint to each subproblem. The trust-region size is adaptively updated according to the behavior of crucial variables. The new subproblems should not be more complex than the original ones, and the convergence properties of the OTR algorithm should be the same as those of Algorithm A. In the present work, the OTR approach is exploited in connection with the “greediness phenomenon” of nonlinear programming. Convergence results for an OTR version of an augmented Lagrangian method for nonconvex constrained optimization are proved, and numerical experiments are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:1:d:10.1007_s10957-011-9815-5
    DOI: 10.1007/s10957-011-9815-5
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    References listed on IDEAS

    as
    1. 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.
    2. J. M. Martínez & L. T. Santos, 1998. "New Theoretical Results on Recursive Quadratic Programming Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 435-454, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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    4. 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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