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A Hybrid Forward–Backward Algorithm and Its Optimization Application

Author

Listed:
  • Liya Liu

    (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Xiaolong Qin

    (Department of Mathematics, Hangzhou Normal University, Hangzhou 31121, China)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, Taichung 40447, Taiwan)

Abstract

In this paper, we study a hybrid forward–backward algorithm for sparse reconstruction. Our algorithm involves descent, splitting and inertial ideas. Under suitable conditions on the algorithm parameters, we establish a strong convergence solution theorem in the framework of Hilbert spaces. Numerical experiments are also provided to illustrate the application in the field of signal processing.

Suggested Citation

  • Liya Liu & Xiaolong Qin & Jen-Chih Yao, 2020. "A Hybrid Forward–Backward Algorithm and Its Optimization Application," Mathematics, MDPI, vol. 8(3), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:447-:d:334563
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    References listed on IDEAS

    as
    1. Yinglin Luo & Meijuan Shang & Bing Tan, 2020. "A General Inertial Viscosity Type Method for Nonexpansive Mappings and Its Applications in Signal Processing," Mathematics, MDPI, vol. 8(2), pages 1-18, February.
    2. Xiao-bo Li & Nan-jing Huang & Qamrul Hasan Ansari & Jen-Chih Yao, 2019. "Convergence Rate of Descent Method with New Inexact Line-Search on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 830-854, March.
    3. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
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