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An active-set algorithm for solving large-scale nonsmooth optimization models with box constraints

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  • Yong Li
  • Gonglin Yuan
  • Zhou Sheng

Abstract

It is well known that the active set algorithm is very effective for smooth box constrained optimization. Many achievements have been obtained in this field. We extend the active set method to nonsmooth box constrained optimization problems, using the Moreau-Yosida regularization technique to make the objective function smooth. A limited memory BFGS method is introduced to decrease the workload of the computer. The presented algorithm has these properties: (1) all iterates are feasible and the sequence of objective functions is decreasing; (2) rapid changes in the active set are allowed; (3) the subproblem is a lower dimensional system of linear equations. The global convergence of the new method is established under suitable conditions and numerical results show that the method is effective for large-scale nonsmooth problems (5,000 variables).

Suggested Citation

  • Yong Li & Gonglin Yuan & Zhou Sheng, 2018. "An active-set algorithm for solving large-scale nonsmooth optimization models with box constraints," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-16, January.
    • Handle: RePEc:plo:pone00:0189290
    DOI: 10.1371/journal.pone.0189290
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    References listed on IDEAS

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    5. 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.
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    Cited by:

    1. Tsegay Giday Woldu & Haibin Zhang & Xin Zhang & Yemane Hailu Fissuh, 2020. "A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 223-238, April.

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