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A Version of Bundle Trust Region Method with Linear Programming

Author

Listed:
  • Shuai Liu

    (South China Normal University Nanhai Campus)

  • Andrew C. Eberhard

    (Royal Melbourne Institute of Technology)

  • Yousong Luo

    (Royal Melbourne Institute of Technology)

Abstract

We present a general version of bundle trust region method for minimizing convex functions. The trust region is constructed by generic $$p$$ p -norm with $$p\in [1,+\infty ]$$ p ∈ [ 1 , + ∞ ] . In each iteration the algorithm solves a subproblem with a constraint involving $$p$$ p -norm. We show the convergence of the generic bundle trust region algorithm. In implementation, the infinity norm is chosen so that a linear programming subproblem is solved in each iteration. Preliminary numerical experiments show that our algorithm performs comparably with the traditional bundle trust region method and has advantages in solving large-scale problems.

Suggested Citation

  • Shuai Liu & Andrew C. Eberhard & Yousong Luo, 2023. "A Version of Bundle Trust Region Method with Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 199(2), pages 639-662, November.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:2:d:10.1007_s10957-023-02293-2
    DOI: 10.1007/s10957-023-02293-2
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    References listed on IDEAS

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    1. W. Ackooij & A. Frangioni & W. Oliveira, 2016. "Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support," Computational Optimization and Applications, Springer, vol. 65(3), pages 637-669, December.
    2. Shuai Liu, 2019. "A simple version of bundle method with linear programming," Computational Optimization and Applications, Springer, vol. 72(2), pages 391-412, March.
    3. R. Andreani & J. M. Martinez & M. L. Schuverdt, 2005. "On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 473-483, May.
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