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A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization

Author

Listed:
  • Xiaoliang Wang

    (School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China)

  • Liping Pang

    (School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China)

  • Qi Wu

    (School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P. R. China)

Abstract

The bundle modification strategy for the convex unconstrained problems was proposed by Alexey et al. [[2007] European Journal of Operation Research, 180(1), 38–47.] whose most interesting feature was the reduction of the calls for the quadratic programming solver. In this paper, we extend the bundle modification strategy to a class of nonconvex nonsmooth constraint problems. Concretely, we adopt the convexification technique to the objective function and constraint function, take the penalty strategy to transfer the modified model into an unconstrained optimization and focus on the unconstrained problem with proximal bundle method and the bundle modification strategies. The global convergence of the corresponding algorithm is proved. The primal numerical results show that the proposed algorithms are promising and effective.

Suggested Citation

  • Xiaoliang Wang & Liping Pang & Qi Wu, 2022. "A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 39(02), pages 1-43, April.
    • Handle: RePEc:wsi:apjorx:v:39:y:2022:i:02:n:s0217595921500159
    DOI: 10.1142/S0217595921500159
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