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A nonmonotone filter method for nonlinear optimization

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  • Chungen Shen
  • Sven Leyffer
  • Roger Fletcher

Abstract

We propose a new nonmonotone filter method to promote global and fast local convergence for sequential quadratic programming algorithms. Our method uses two filters: a standard, global g-filter for global convergence, and a local nonmonotone l-filter that allows us to establish fast local convergence. We show how to switch between the two filters efficiently, and we prove global and superlinear local convergence. A special feature of the proposed method is that it does not require second-order correction steps. We present preliminary numerical results comparing our implementation with a classical filter SQP method. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Chungen Shen & Sven Leyffer & Roger Fletcher, 2012. "A nonmonotone filter method for nonlinear optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 583-607, July.
    • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:583-607
    DOI: 10.1007/s10589-011-9430-2
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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    Cited by:

    1. Zhongwen Chen & Yu-Hong Dai & Jiangyan Liu, 2020. "A penalty-free method with superlinear convergence for equality constrained optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 801-833, July.
    2. M. Fernanda P. Costa & Ana Maria A. C. Rocha & Edite M. G. P. Fernandes, 2018. "Filter-based DIRECT method for constrained global optimization," Journal of Global Optimization, Springer, vol. 71(3), pages 517-536, July.
    3. Chungen Shen & Lei-Hong Zhang & Wei Liu, 2016. "A stabilized filter SQP algorithm for nonlinear programming," Journal of Global Optimization, Springer, vol. 65(4), pages 677-708, August.
    4. Ana Rocha & M. Costa & Edite Fernandes, 2014. "A filter-based artificial fish swarm algorithm for constrained global optimization: theoretical and practical issues," Journal of Global Optimization, Springer, vol. 60(2), pages 239-263, October.
    5. Chungen Shen & Lei-Hong Zhang & Bo Wang & Wenqiong Shao, 2014. "Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization," Computational Optimization and Applications, Springer, vol. 59(3), pages 435-473, December.
    6. Sven Leyffer & Charlie Vanaret, 2020. "An augmented Lagrangian filter method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 343-376, October.
    7. Pei, Yonggang & Zhu, Detong, 2016. "Local convergence of a trust-region algorithm with line search filter technique for nonlinear constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 797-808.
    8. E. Birgin & J. Martínez & L. Prudente, 2015. "Optimality properties of an Augmented Lagrangian method on infeasible problems," Computational Optimization and Applications, Springer, vol. 60(3), pages 609-631, April.

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