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Solving nonnegative sparsity-constrained optimization via DC quadratic-piecewise-linear approximations

Author

Listed:
  • Chungen Shen

    (University of Shanghai for Science and Technology)

  • Xiao Liu

    (University of Shanghai for Science and Technology)

Abstract

In this paper, we propose a novel algorithm that is based on quadratic-piecewise-linear approximations of DC functions to solve nonnegative sparsity-constrained optimization. A penalized DC (difference of two convex functions) formulation is proved to be equivalent to the original problem under a suitable penalty parameter. We employ quadratic-piecewise-linear approximations to the two parts of the DC objective function, resulting in a nonconvex subproblem. This is the key ingredient of our main algorithm. This nonconvex subproblem can be solved by a globally convergent alternating variable algorithm. Under some mild conditions, we prove that the proposed main algorithm for the penalized problem is globally convergent. Some preliminary numerical results on the sparse nonnegative least squares and logistic regression problems demonstrate the efficiency of our algorithm.

Suggested Citation

  • Chungen Shen & Xiao Liu, 2021. "Solving nonnegative sparsity-constrained optimization via DC quadratic-piecewise-linear approximations," Journal of Global Optimization, Springer, vol. 81(4), pages 1019-1055, December.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:4:d:10.1007_s10898-021-01028-9
    DOI: 10.1007/s10898-021-01028-9
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    References listed on IDEAS

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    1. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2018. "Minimizing Piecewise-Concave Functions Over Polyhedra," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 580-597, May.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico & Adil M. Bagirov, 2018. "Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations," Journal of Global Optimization, Springer, vol. 71(1), pages 37-55, May.
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    5. Adil Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2014. "Introduction to Nonsmooth Optimization," Springer Books, Springer, edition 127, number 978-3-319-08114-4, December.
    6. Bo Wen & Xiaojun Chen & Ting Kei Pong, 2018. "A proximal difference-of-convex algorithm with extrapolation," Computational Optimization and Applications, Springer, vol. 69(2), pages 297-324, March.
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