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Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods

Author

Listed:
  • Hao Wang

    (ShanghaiTech University)

  • Fan Zhang

    (ShanghaiTech University
    University of Chinese Academy of Sciences
    Chinese Academy of Sciences)

  • Yuanming Shi

    (ShanghaiTech University)

  • Yaohua Hu

    (Shenzhen University)

Abstract

We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a wide range of applications. We design a general algorithmic framework of iteratively reweighted algorithms for solving the proposed nonconvex and nonsmooth sparse optimization problems, which solves a sequence of weighted convex regularization problems with adaptively updated weights. First-order optimality condition is derived and global convergence results are provided under loose assumptions, making our theoretical results a practical tool for analyzing a family of various reweighted algorithms. The effectiveness and efficiency of our proposed formulation and the algorithms are demonstrated in numerical experiments on various sparse optimization problems.

Suggested Citation

  • Hao Wang & Fan Zhang & Yuanming Shi & Yaohua Hu, 2021. "Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods," Journal of Global Optimization, Springer, vol. 81(3), pages 717-748, November.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:3:d:10.1007_s10898-021-01093-0
    DOI: 10.1007/s10898-021-01093-0
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    References listed on IDEAS

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    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    Cited by:

    1. Shuqin Sun & Ting Kei Pong, 2023. "Doubly iteratively reweighted algorithm for constrained compressed sensing models," Computational Optimization and Applications, Springer, vol. 85(2), pages 583-619, June.

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