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Accelerated iterative hard thresholding algorithm for $$l_0$$l0 regularized regression problem

Author

Listed:
  • Fan Wu

    (Harbin Institute of Technology)

  • Wei Bian

    (Harbin Institute of Technology)

Abstract

In this paper, we propose an accelerated iterative hard thresholding algorithm for solving the $$l_0$$l0 regularized box constrained regression problem. We substantiate that there exists a threshold, if the extrapolation coefficients are chosen below this threshold, the proposed algorithm is equivalent to the accelerated proximal gradient algorithm for solving a corresponding constrained convex problem after finite iterations. Under some proper conditions, we get that the sequence generated by the proposed algorithm is convergent to a local minimizer of the $$l_0$$l0 regularized problem, which satisfies a desired lower bound. Moreover, when the data fitting function satisfies the error bound condition, we prove that both the iterate sequence and the corresponding sequence of objective function values are R-linearly convergent. Finally, we use several numerical experiments to verify our theoretical results.

Suggested Citation

  • Fan Wu & Wei Bian, 2020. "Accelerated iterative hard thresholding algorithm for $$l_0$$l0 regularized regression problem," Journal of Global Optimization, Springer, vol. 76(4), pages 819-840, April.
    • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-019-00826-6
    DOI: 10.1007/s10898-019-00826-6
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    References listed on IDEAS

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    Cited by:

    1. Dongdong Zhang & Shaohua Pan & Shujun Bi & Defeng Sun, 2023. "Zero-norm regularized problems: equivalent surrogates, proximal MM method and statistical error bound," Computational Optimization and Applications, Springer, vol. 86(2), pages 627-667, November.

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