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Asymmetric forward–backward–adjoint splitting for solving monotone inclusions involving three operators

Author

Listed:
  • Puya Latafat

    (KU Leuven
    IMT School for Advanced Studies Lucca)

  • Panagiotis Patrinos

    (KU Leuven)

Abstract

In this work we propose a new splitting technique, namely Asymmetric Forward–Backward–Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Our scheme can not be recovered from existing operator splitting methods, while classical methods like Douglas–Rachford and Forward–Backward splitting are special cases of the new algorithm. Asymmetric preconditioning is the main feature of Asymmetric Forward–Backward–Adjoint splitting, that allows us to unify, extend and shed light on the connections between many seemingly unrelated primal-dual algorithms for solving structured convex optimization problems proposed in recent years. One important special case leads to a Douglas–Rachford type scheme that includes a third cocoercive operator.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:68:y:2017:i:1:d:10.1007_s10589-017-9909-6
    DOI: 10.1007/s10589-017-9909-6
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    References listed on IDEAS

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    1. Min Li & Defeng Sun & Kim-Chuan Toh, 2015. "A Convergent 3-Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex Block," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-19.
    2. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
    3. 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.
    4. Deren Han & Xiaoming Yuan, 2012. "A Note on the Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 227-238, October.
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    Cited by:

    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. Yekini Shehu & Lulu Liu & Qiao-Li Dong & Jen-Chih Yao, 2022. "A Relaxed Forward-Backward-Forward Algorithm with Alternated Inertial Step: Weak and Linear Convergence," Networks and Spatial Economics, Springer, vol. 22(4), pages 959-990, December.
    3. Yawei Shi & Liang Ran & Jialong Tang & Xiangzhao Wu, 2022. "Distributed Optimization Algorithm for Composite Optimization Problems with Non-Smooth Function," Mathematics, MDPI, vol. 10(17), pages 1-17, September.
    4. Ernest K. Ryu & Bằng Công Vũ, 2020. "Finding the Forward-Douglas–Rachford-Forward Method," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 858-876, March.
    5. 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.

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