IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i10p922-d273227.html

Convergence of Two Splitting Projection Algorithms in Hilbert Spaces

Author

Listed:
  • Marwan A. Kutbi

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Abdul Latif

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Xiaolong Qin

    (Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

Abstract

The aim of this present paper is to study zero points of the sum of two maximally monotone mappings and fixed points of a non-expansive mapping. Two splitting projection algorithms are introduced and investigated for treating the zero and fixed point problems. Possible computational errors are taken into account. Two convergence theorems are obtained and applications are also considered in Hilbert spaces

Suggested Citation

  • Marwan A. Kutbi & Abdul Latif & Xiaolong Qin, 2019. "Convergence of Two Splitting Projection Algorithms in Hilbert Spaces," Mathematics, MDPI, vol. 7(10), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:922-:d:273227
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/10/922/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/10/922/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
    2. S. Takahashi & W. Takahashi & M. Toyoda, 2010. "Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 27-41, October.
    3. Jonathan Eckstein & Michael C. Ferris, 1998. "Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control," INFORMS Journal on Computing, INFORMS, vol. 10(2), pages 218-235, May.
    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. Felipe Alvarez & Miguel Carrasco & Karine Pichard, 2005. "Convergence of a Hybrid Projection-Proximal Point Algorithm Coupled with Approximation Methods in Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 966-984, November.
    2. Mauricio Romero Sicre, 2020. "On the complexity of a hybrid proximal extragradient projective method for solving monotone inclusion problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 991-1019, July.
    3. Konstantinos A. Oikonomidis & Alexander Bodard & Emanuel Laude & Panagiotis Patrinos, 2026. "Global convergence analysis of the power proximal point and augmented Lagrangian method," Computational Optimization and Applications, Springer, vol. 93(2), pages 617-649, March.
    4. Jean-Pierre Crouzeix & Abdelhak Hassouni & Eladio Ocaña, 2023. "A Short Note on the Twice Differentiability of the Marginal Function of a Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 857-867, August.
    5. Liang Chen & Anping Liao, 2020. "On the Convergence Properties of a Second-Order Augmented Lagrangian Method for Nonlinear Programming Problems with Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 248-265, October.
    6. Stefano Cipolla & Jacek Gondzio, 2023. "Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1061-1103, June.
    7. Yonghong Yao & Yeong-Cheng Liou & Ngai-Ching Wong, 2013. "Superimposed optimization methods for the mixed equilibrium problem and variational inclusion," Journal of Global Optimization, Springer, vol. 57(3), pages 935-950, November.
    8. Bingsheng He & Li-Zhi Liao & Xiang Wang, 2012. "Proximal-like contraction methods for monotone variational inequalities in a unified framework I: Effective quadruplet and primary methods," Computational Optimization and Applications, Springer, vol. 51(2), pages 649-679, March.
    9. Brecht Evens & Puya Latafat & Panagiotis Patrinos, 2025. "Convergence of the Chambolle–Pock Algorithm in the Absence of Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-45, July.
    10. Teemu Pennanen & Markku Kallio, 2006. "A splitting method for stochastic programs," Annals of Operations Research, Springer, vol. 142(1), pages 259-268, February.
    11. Xiaoling Fu, 2013. "A General Self‐Adaptive Relaxed‐PPA Method for Convex Programming with Linear Constraints," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    12. Darinka Dentcheva & Gabriela Martinez & Eli Wolfhagen, 2016. "Augmented Lagrangian Methods for Solving Optimization Problems with Stochastic-Order Constraints," Operations Research, INFORMS, vol. 64(6), pages 1451-1465, December.
    13. Gui-Hua Lin & Zhen-Ping Yang & Hai-An Yin & Jin Zhang, 2023. "A dual-based stochastic inexact algorithm for a class of stochastic nonsmooth convex composite problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 669-710, November.
    14. Penghe Zhang & Naihua Xiu & Ziyan Luo, 2024. "Zero-One Composite Optimization: Lyapunov Exact Penalty and a Globally Convergent Inexact Augmented Lagrangian Method," Mathematics of Operations Research, INFORMS, vol. 49(4), pages 2602-2625, November.
    15. Xiaoming Yuan, 2011. "An improved proximal alternating direction method for monotone variational inequalities with separable structure," Computational Optimization and Applications, Springer, vol. 49(1), pages 17-29, May.
    16. Liwei Zhang & Yule Zhang & Xiantao Xiao & Jia Wu, 2023. "Stochastic Approximation Proximal Method of Multipliers for Convex Stochastic Programming," Mathematics of Operations Research, INFORMS, vol. 48(1), pages 177-193, February.
    17. Zhu, Daoli & Marcotte, Patrice, 1995. "Coupling the auxiliary problem principle with descent methods of pseudoconvex programming," European Journal of Operational Research, Elsevier, vol. 83(3), pages 670-685, June.
    18. Jae Ug Jeong, 2015. "Convergence Theorems of Common Elements for Pseudocontractive Mappings and Monotone Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    19. Guo, Zhaomiao & Fan, Yueyue, 2017. "A Stochastic Multi-Agent Optimization Model for Energy Infrastructure Planning Under Uncertainty and Competition," Institute of Transportation Studies, Working Paper Series qt89s5s8hn, Institute of Transportation Studies, UC Davis.
    20. Mohammad Akram & Mohammad Dilshad & Aysha Khan & Sumit Chandok & Izhar Ahmad, 2023. "Convergence Analysis for Generalized Yosida Inclusion Problem with Applications," Mathematics, MDPI, vol. 11(6), pages 1-19, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:7:y:2019:i:10:p:922-:d:273227. 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 The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (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.