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Non-monotone inexact restoration method for nonlinear programming

Author

Listed:
  • Juliano B. Francisco

    (Universidade Federal de Santa Catarina)

  • Douglas S. Gonçalves

    (Universidade Federal de Santa Catarina)

  • Fermín S. V. Bazán

    (Universidade Federal de Santa Catarina)

  • Lila L. T. Paredes

    (Universidad Nacional Mayor de San Marcos)

Abstract

This paper deals with a new variant of the inexact restoration method of Fischer and Friedlander (Comput Optim Appl 46:333–346, 2010) for nonlinear programming. We propose an algorithm that replaces the monotone line search performed in the tangent phase by a non-monotone one, using the sharp Lagrangian as merit function. Convergence to feasible points satisfying the convex approximate gradient projection condition is proved under mild assumptions. Numerical results on representative test problems show that the proposed approach outperforms the monotone version when a suitable non-monotone parameter is chosen and is also competitive against other globalization strategies for inexact restoration.

Suggested Citation

  • Juliano B. Francisco & Douglas S. Gonçalves & Fermín S. V. Bazán & Lila L. T. Paredes, 2020. "Non-monotone inexact restoration method for nonlinear programming," Computational Optimization and Applications, Springer, vol. 76(3), pages 867-888, July.
    • Handle: RePEc:spr:coopap:v:76:y:2020:i:3:d:10.1007_s10589-019-00129-2
    DOI: 10.1007/s10589-019-00129-2
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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. 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.
    3. Y. H. Dai, 2002. "On the Nonmonotone Line Search," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 315-330, February.
    4. Roberto Andreani & José Mario Martínez & Alberto Ramos & Paulo J. S. Silva, 2018. "Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 693-717, August.
    5. 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.
    6. R. Andreani & S. Castro & J. Chela & A. Friedlander & S. Santos, 2009. "An inexact-restoration method for nonlinear bilevel programming problems," Computational Optimization and Applications, Springer, vol. 43(3), pages 307-328, July.
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