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An effective adaptive trust region algorithm for nonsmooth minimization

Author

Listed:
  • Zhou Sheng

    (Guangxi University)

  • Gonglin Yuan

    (Guangxi University)

Abstract

In this paper, an adaptive trust region algorithm that uses Moreau–Yosida regularization is proposed for solving nonsmooth unconstrained optimization problems. The proposed algorithm combines a modified secant equation with the BFGS update formula and an adaptive trust region radius, and the new trust region radius utilizes not only the function information but also the gradient information. The global convergence and the local superlinear convergence of the proposed algorithm are proven under suitable conditions. Finally, the preliminary results from comparing the proposed algorithm with some existing algorithms using numerical experiments reveal that the proposed algorithm is quite promising for solving nonsmooth unconstrained optimization problems.

Suggested Citation

  • Zhou Sheng & Gonglin Yuan, 2018. "An effective adaptive trust region algorithm for nonsmooth minimization," Computational Optimization and Applications, Springer, vol. 71(1), pages 251-271, September.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:1:d:10.1007_s10589-018-9999-9
    DOI: 10.1007/s10589-018-9999-9
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    References listed on IDEAS

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    1. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    2. Zhaocheng Cui & Boying Wu, 2012. "A new modified nonmonotone adaptive trust region method for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 53(3), pages 795-806, December.
    3. Shi, Zhenjun & Wang, Shengquan, 2011. "Nonmonotone adaptive trust region method," European Journal of Operational Research, Elsevier, vol. 208(1), pages 28-36, January.
    4. E. Polak & J. O. Royset, 2003. "Algorithms for Finite and Semi-Infinite Min–Max–Min Problems Using Adaptive Smoothing Techniques," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 421-457, December.
    5. Adil Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2014. "Introduction to Nonsmooth Optimization," Springer Books, Springer, edition 127, number 978-3-319-08114-4, October.
    6. Zengru Cui & Gonglin Yuan & Zhou Sheng & Wenjie Liu & Xiaoliang Wang & Xiabin Duan, 2015. "A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-15, October.
    7. A. I. Rauf & M. Fukushima, 2000. "Globally Convergent BFGS Method for Nonsmooth Convex Optimization1," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 539-558, March.
    8. Gonglin Yuan & Zhou Sheng & Wenjie Liu, 2016. "The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-15, October.
    9. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    10. Z. Akbari & R. Yousefpour & M. Reza Peyghami, 2015. "A New Nonsmooth Trust Region Algorithm for Locally Lipschitz Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 733-754, March.
    11. Gonglin Yuan & Zengxin Wei & Zhongxing Wang, 2013. "Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization," Computational Optimization and Applications, Springer, vol. 54(1), pages 45-64, January.
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