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An Active Set Modified Polak–Ribiére–Polyak Method for Large-Scale Nonlinear Bound Constrained Optimization

Author

Listed:
  • Wanyou Cheng

    (Dongguan University of Technology)

  • Donghui Li

    (South China Normal University)

Abstract

In this paper, we propose an active set modified Polak–Ribiére–Polyak method for solving large-scale optimization with simple bounds on the variables. The active set is guessed by an identification technique at each iteration and the recently developed modified Polak–Ribiére–Polyak method is used to update the variables with indices outside of the active set. Under appropriate conditions, we show that the proposed method is globally convergent. Numerical experiments are presented using box constrained problems in the CUTEr test problem libraries.

Suggested Citation

  • Wanyou Cheng & Donghui Li, 2012. "An Active Set Modified Polak–Ribiére–Polyak Method for Large-Scale Nonlinear Bound Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 1084-1094, December.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:3:d:10.1007_s10957-012-0091-9
    DOI: 10.1007/s10957-012-0091-9
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    References listed on IDEAS

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    1. Oleg Burdakov & José Martínez & Elvio Pilotta, 2002. "A Limited-Memory Multipoint Symmetric Secant Method for Bound Constrained Optimization," Annals of Operations Research, Springer, vol. 117(1), pages 51-70, November.
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    Cited by:

    1. XiaoLiang Dong & Deren Han & Zhifeng Dai & Lixiang Li & Jianguang Zhu, 2018. "An Accelerated Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 944-961, December.
    2. Andrea Cristofari & Marianna Santis & Stefano Lucidi & Francesco Rinaldi, 2017. "A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 369-401, February.
    3. Nikhil Devanathan & Stephen Boyd, 2024. "Polyak Minorant Method for Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 203(3), pages 2263-2282, December.
    4. Dong, Xiao Liang & Liu, Hong Wei & He, Yu Bo, 2015. "New version of the three-term conjugate gradient method based on spectral scaling conjugacy condition that generates descent search direction," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 606-617.
    5. XiaoLiang Dong & Hongwei Liu & Yubo He, 2015. "A Self-Adjusting Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 225-241, April.

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