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An Inexact Projected Gradient Method for Sparsity-Constrained Quadratic Measurements Regression

Author

Listed:
  • Jun Fan

    (Institute of Mathematics, Hebei University of Technology, Tianjin 300401, P. R. China)

  • Liqun Wang

    (Department of Statistics, University of Manitoba, Winnipeg, R3T 2N2, Canada)

  • Ailing Yan

    (Institute of Mathematics, Hebei University of Technology, Tianjin 300401, P. R. China)

Abstract

In this paper, we employ the sparsity-constrained least squares method to reconstruct sparse signals from the noisy measurements in high-dimensional case, and derive the existence of the optimal solution under certain conditions. We propose an inexact sparse-projected gradient method for numerical computation and discuss its convergence. Moreover, we present numerical results to demonstrate the efficiency of the proposed method.

Suggested Citation

  • Jun Fan & Liqun Wang & Ailing Yan, 2019. "An Inexact Projected Gradient Method for Sparsity-Constrained Quadratic Measurements Regression," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-21, April.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:02:n:s0217595919400086
    DOI: 10.1142/S0217595919400086
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    Citations

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    Cited by:

    1. A. A. Aguiar & O. P. Ferreira & L. F. Prudente, 2023. "Inexact gradient projection method with relative error tolerance," Computational Optimization and Applications, Springer, vol. 84(2), pages 363-395, March.
    2. O. P. Ferreira & M. Lemes & L. F. Prudente, 2022. "On the inexact scaled gradient projection method," Computational Optimization and Applications, Springer, vol. 81(1), pages 91-125, January.

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