IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i3p447-d334563.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/3/447/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/3/447/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pawicha Phairatchatniyom & Poom Kumam & Yeol Je Cho & Wachirapong Jirakitpuwapat & Kanokwan Sitthithakerngkiet, 2019. "The Modified Inertial Iterative Algorithm for Solving Split Variational Inclusion Problem for Multi-Valued Quasi Nonexpansive Mappings with Some Applications," Mathematics, MDPI, vol. 7(6), pages 1-22, June.
    2. Suthep Suantai & Suparat Kesornprom & Prasit Cholamjiak, 2019. "Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions," Mathematics, MDPI, vol. 7(8), pages 1-17, August.
    3. Fabiana R. Oliveira & Orizon P. Ferreira & Gilson N. Silva, 2019. "Newton’s method with feasible inexact projections for solving constrained generalized equations," Computational Optimization and Applications, Springer, vol. 72(1), pages 159-177, January.
    4. Sitthithakerngkiet, Kanokwan & Deepho, Jitsupa & Kumam, Poom, 2015. "A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 986-1001.
    5. Thidaporn Seangwattana & Somyot Plubtieng & Kanokwan Sitthithakerngkiet, 2021. "A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 614-628, June.
    6. Bunyawee Chaloemyotphong & Atid Kangtunyakarn, 2019. "Modified Halpern Iterative Method for Solving Hierarchical Problem and Split Combination of Variational Inclusion Problem in Hilbert Space," Mathematics, MDPI, vol. 7(11), pages 1-26, November.
    7. Pingjing Xia & Gang Cai & Qiao-Li Dong, 2023. "A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(4), pages 931-952, December.
    8. repec:wsi:jeapmx:v:20:y:2018:i:04:n:s0219198918500056 is not listed on IDEAS
    9. Che, Haitao & Li, Meixia, 2016. "The conjugate gradient method for split variational inclusion and constrained convex minimization problems," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 426-438.
    10. Shih-sen Chang & Jen-Chih Yao & Ching-Feng Wen & Liang-cai Zhao, 2020. "On the Split Equality Fixed Point Problem of Quasi-Pseudo-Contractive Mappings Without A Priori Knowledge of Operator Norms with Applications," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 343-360, May.
    11. Vo Minh Tam & Nguyen Hung & Zhenhai Liu & Jen Chih Yao, 2022. "Levitin–Polyak Well-Posedness by Perturbations for the Split Hemivariational Inequality Problem on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 684-706, November.
    12. Kumar, Ajay & Thakur, Balwant Singh & Postolache, Mihai, 2024. "Dynamic stepsize iteration process for solving split common fixed point problems with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 498-511.
    13. Shih-sen Chang & Lin Wang & Xiong Rui Wang & Gang Wang, 2015. "General Split Equality Equilibrium Problems with Application to Split Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 377-390, August.
    14. Shipra Singh & Savin Treanţă, 2021. "Characterization results of weak sharp solutions for split variational inequalities with application to traffic analysis," Annals of Operations Research, Springer, vol. 302(1), pages 265-287, July.
    15. Abdellatif Moudafi, 2014. "Computing the resolvent of composite operators," Documents de Travail 2014-02, CEREGMIA, Université des Antilles et de la Guyane.
    16. Le Hai Yen & Le Dung Muu & Nguyen Thi Thanh Huyen, 2016. "An algorithm for a class of split feasibility problems: application to a model in electricity production," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 549-565, December.
    17. Liya Liu & Xiaolong Qin & Jen-Chih Yao, 2020. "Strong Convergent Theorems Governed by Pseudo-Monotone Mappings," Mathematics, MDPI, vol. 8(8), pages 1-15, July.
    18. Yan Tang & Yeol Je Cho, 2019. "Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems," Mathematics, MDPI, vol. 7(3), pages 1-25, March.
    19. 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.
    20. Mujahid Abbas & Yusuf Ibrahim & Abdul Rahim Khan & Manuel De la Sen, 2019. "Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in CAT (0) Spaces," Mathematics, MDPI, vol. 7(8), pages 1-14, August.
    21. Andreea Bejenaru & Mihai Postolache, 2022. "New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process," Mathematics, MDPI, vol. 10(19), pages 1-16, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:447-:d:334563. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.