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A new splitting method for systems of monotone inclusions in Hilbert spaces

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  • Dong, Yunda

Abstract

In this article, we consider the problem of finding a zero of systems of monotone inclusions in real Hilbert spaces. Furthermore, each monotone inclusion consists of three operators and the third is linearly composed. We suggest a splitting method for solving them: At each iteration, for each monotone inclusion, it mainly needs computations of three resolvents for individual operator. This method can be viewed as a powerful extension of the classical Douglas–Rachford splitting. Under the weakest possible assumptions, by introducing and using the characteristic operator, we analyze its weak convergence. The most striking feature is that it merely requires each scaling factor for individual operator be positive. Numerical results indicate practical usefulness of this method, together with its special cases, in solving our test problems of separable structure.

Suggested Citation

  • Dong, Yunda, 2023. "A new splitting method for systems of monotone inclusions in Hilbert spaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 518-537.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:518-537
    DOI: 10.1016/j.matcom.2022.06.023
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    References listed on IDEAS

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    1. Yunda Dong, 2021. "Weak convergence of an extended splitting method for monotone inclusions," Journal of Global Optimization, Springer, vol. 79(1), pages 257-277, January.
    2. Laurent Condat, 2013. "A Primal–Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 460-479, August.
    3. Patrick R. Johnstone & Jonathan Eckstein, 2021. "Single-forward-step projective splitting: exploiting cocoercivity," Computational Optimization and Applications, Springer, vol. 78(1), pages 125-166, January.
    4. Puya Latafat & Panagiotis Patrinos, 2017. "Asymmetric forward–backward–adjoint splitting for solving monotone inclusions involving three operators," Computational Optimization and Applications, Springer, vol. 68(1), pages 57-93, September.
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