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A simple version of bundle method with linear programming

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  • Shuai Liu

    (IMECC/UNICAMP)

Abstract

Bundle methods have been well studied in nonsmooth optimization. In most of the bundle methods developed thus far (traditional bundle methods), at least one quadratic programming subproblem needs to be solved in each iteration. In this paper, a simple version of bundle method with linear programming is proposed. In each iteration, a cutting-plane model subject to a constraint constructed by an infinity norm is minimized. Without line search or trust region techniques, the convergence of the method can be shown. Additionally, the infinity norm in the constraint can be generalized to $$p$$ p -norm. Preliminary numerical experiments show the potential advantage of the proposed method for solving large scale problems.

Suggested Citation

  • Shuai Liu, 2019. "A simple version of bundle method with linear programming," Computational Optimization and Applications, Springer, vol. 72(2), pages 391-412, March.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:2:d:10.1007_s10589-018-0048-5
    DOI: 10.1007/s10589-018-0048-5
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    References listed on IDEAS

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    Cited by:

    1. Tang, Chunming & Liu, Shuai & Jian, Jinbao & Ou, Xiaomei, 2020. "A multi-step doubly stabilized bundle method for nonsmooth convex optimization," Applied Mathematics and Computation, Elsevier, vol. 376(C).

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