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A discretization algorithm for nonsmooth convex semi-infinite programming problems based on bundle methods

Author

Listed:
  • Li-Ping Pang

    (Dalian University of Technology)

  • Qi Wu

    (Dalian University of Technology)

  • Jin-He Wang

    (Huzhou University)

  • Qiong Wu

    (Dalian University of Technology)

Abstract

We propose a discretization algorithm for solving a class of nonsmooth convex semi-infinite programming problems that is based on a bundle method. Instead of employing the inexact calculation to evaluate the lower level problem, we shall carry out a discretization scheme. The discretization method is used to get a number of discretized problems which are solved by the bundle method. In particular, the subproblem used to generate a new point is independent of the number of constraints of the discretized problem. We apply a refinement-step which can be used to guarantee the convergence of the bundle method for the discretized problems as well as reduce the cost of the evaluations for the constraint functions during iteration. In addition we adopt an aggregation technique to manage the bundle information coming from previous steps. Both theoretical convergence analysis and preliminary computational results are reported. The results obtained have shown the good performance of the new algorithm.

Suggested Citation

  • Li-Ping Pang & Qi Wu & Jin-He Wang & Qiong Wu, 2020. "A discretization algorithm for nonsmooth convex semi-infinite programming problems based on bundle methods," Computational Optimization and Applications, Springer, vol. 76(1), pages 125-153, May.
    • Handle: RePEc:spr:coopap:v:76:y:2020:i:1:d:10.1007_s10589-020-00170-6
    DOI: 10.1007/s10589-020-00170-6
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    References listed on IDEAS

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    1. Sanjay Mehrotra & David Papp, 2013. "A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization," Papers 1306.3437, arXiv.org, revised Aug 2014.
    2. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    3. Takayuki Okuno & Masao Fukushima, 2014. "Local reduction based SQP-type method for semi-infinite programs with an infinite number of second-order cone constraints," Journal of Global Optimization, Springer, vol. 60(1), pages 25-48, September.
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    5. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    6. Adil Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2014. "Introduction to Nonsmooth Optimization," Springer Books, Springer, edition 127, number 978-3-319-08114-4, December.
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