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Weighted thresholding homotopy method for sparsity constrained optimization

Author

Listed:
  • Wenxing Zhu

    (Fuzhou University)

  • Huating Huang

    (Fuzhou University)

  • Lanfan Jiang

    (Fuzhou University)

  • Jianli Chen

    (Fuzhou University)

Abstract

We propose in this paper a novel weighted thresholding method for the sparsity-constrained optimization problem. By reformulating the problem equivalently as a mixed-integer programming, we investigate the Lagrange duality with respect to an $$l_1$$ l 1 -norm constraint and show the strong duality property. Then we derive a weighted thresholding method for the inner Lagrangian problem, and analyze its convergence. In addition, we give an error bound of the solution under some assumptions. Further, based on the proposed method, we develop a homotopy algorithm with varying sparsity level and Lagrange multiplier, and prove that the algorithm converges to an L-stationary point of the primal problem under some conditions. Computational experiments show that the proposed algorithm is competitive with state-of-the-art methods for the sparsity-constrained optimization problem.

Suggested Citation

  • Wenxing Zhu & Huating Huang & Lanfan Jiang & Jianli Chen, 2022. "Weighted thresholding homotopy method for sparsity constrained optimization," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1924-1952, October.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00563-7
    DOI: 10.1007/s10878-020-00563-7
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    References listed on IDEAS

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