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General splitting methods with linearization for the split feasibility problem

Author

Listed:
  • Qiao-Li Dong

    (Civil Aviation University of China)

  • Songnian He

    (Civil Aviation University of China)

  • Michael Th. Rassias

    (University of Zurich
    Moscow Institute of Physics and Technology)

Abstract

In this article, we introduce a general splitting method with linearization to solve the split feasibility problem and propose a way of selecting the stepsizes such that the implementation of the method does not need any prior information about the operator norm. We present the constant and adaptive relaxation parameters, and the latter is “optimal” in theory. These ways of selecting stepsizes and relaxation parameters are also practised to the relaxed splitting method with linearization where the two closed convex sets are both level sets of convex functions. The weak convergence of two proposed methods is established under standard conditions and the linear convergence of the general splitting method with linearization is analyzed. The numerical examples are presented to illustrate the advantage of our methods by comparing with other methods.

Suggested Citation

  • Qiao-Li Dong & Songnian He & Michael Th. Rassias, 2021. "General splitting methods with linearization for the split feasibility problem," Journal of Global Optimization, Springer, vol. 79(4), pages 813-836, April.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:4:d:10.1007_s10898-020-00963-3
    DOI: 10.1007/s10898-020-00963-3
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    References listed on IDEAS

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    1. Le Hai Yen & Nguyen Thi Thanh Huyen & Le Dung Muu, 2019. "A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models," Journal of Global Optimization, Springer, vol. 73(4), pages 849-868, April.
    2. Min Li & Zhongming Wu, 2019. "Convergence Analysis of the Generalized Splitting Methods for a Class of Nonconvex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 535-565, November.
    3. Biao Qu & Changyu Wang & Naihua Xiu, 2017. "Analysis on Newton projection method for the split feasibility problem," Computational Optimization and Applications, Springer, vol. 67(1), pages 175-199, May.
    4. Francisco J. Aragón Artacho & Rubén Campoy & Veit Elser, 2020. "An enhanced formulation for solving graph coloring problems with the Douglas–Rachford algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 383-403, June.
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    Cited by:

    1. Teeranush Suebcharoen & Raweerote Suparatulatorn & Tanadon Chaobankoh & Khwanchai Kunwai & Thanasak Mouktonglang, 2024. "An Inertial Relaxed CQ Algorithm with Two Adaptive Step Sizes and Its Application for Signal Recovery," Mathematics, MDPI, vol. 12(15), pages 1-16, August.
    2. Yuanheng Wang & Tiantian Xu & Jen-Chih Yao & Bingnan Jiang, 2022. "Self-Adaptive Method and Inertial Modification for Solving the Split Feasibility Problem and Fixed-Point Problem of Quasi-Nonexpansive Mapping," Mathematics, MDPI, vol. 10(9), pages 1-15, May.

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