IDEAS home Printed from https://ideas.repec.org/a/ibn/jmrjnl/v10y2018i2p66.html
   My bibliography  Save this article

Convergence Theorems of Modified Proximal Algorithms for Asymptotical Quasi-nonexpansive Mappings in CAT(0) Spaces

Author

Listed:
  • Shengquan Weng
  • Dingping Wu

Abstract

In this paper, a new modified proximal point algorithm involving fixed point iterates of a finite number of asymptotically quasi-nonexpansive mappings in $CAT(0)$ spaces is proposed and been proved for the existence of a sequence generated by our iterative process converging to a minimizer of a convex function and a commen fixed point of a finite number of asymptotically quasi-nonexpansive mappings.

Suggested Citation

  • Shengquan Weng & Dingping Wu, 2018. "Convergence Theorems of Modified Proximal Algorithms for Asymptotical Quasi-nonexpansive Mappings in CAT(0) Spaces," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(2), pages 66-76, April.
    • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:2:p:66
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/73930/40677
    Download Restriction: no
    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/73930
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
    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. Rattanaporn Wangkeeree & Rabian Wangkeeree, 2013. "The general iterative methods for nonexpansive semigroups in Banach spaces," Journal of Global Optimization, Springer, vol. 55(2), pages 417-436, February.
    2. Eric U. Ofoedu, 2013. "A General Approximation Scheme for Solutions of Various Problems in Fixed Point Theory," International Journal of Analysis, Hindawi, vol. 2013, pages 1-18, January.
    3. Uthai Kamraksa & Rabian Wangkeeree, 2011. "Generalized equilibrium problems and fixed point problems for nonexpansive semigroups in Hilbert spaces," Journal of Global Optimization, Springer, vol. 51(4), pages 689-714, December.
    4. Giuseppe Marino & Hong-Kun Xu, 2011. "Explicit Hierarchical Fixed Point Approach to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 61-78, April.
    5. Himanshu Baranwal & Ravindra Kishor Bisht & Arya Kumar Bedabrata Chand & Jen-Chih Yao, 2024. "Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric," Mathematics, MDPI, vol. 12(18), pages 1-30, September.
    6. ChangAn Tian & Yisheng Song, 2013. "Strong convergence of a regularization method for Rockafellar’s proximal point algorithm," Journal of Global Optimization, Springer, vol. 55(4), pages 831-837, April.
    7. Haiyun Zhou & Peiyuan Wang, 2014. "A Simpler Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 716-727, June.
    8. Phayap Katchang & Poom Kumam, 2013. "An iterative algorithm for common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings with optimization problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1563-1589, August.
    9. Jeong, Jae Ug, 2016. "Generalized viscosity approximation methods for mixed equilibrium problems and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 168-180.
    10. Scott Kolodziej & Pedro Castro & Ignacio Grossmann, 2013. "Global optimization of bilinear programs with a multiparametric disaggregation technique," Journal of Global Optimization, Springer, vol. 57(4), pages 1039-1063, December.
    11. Jamil, Muhammad Ahmad & Zubair, Syed M., 2017. "Design and analysis of a forward feed multi-effect mechanical vapor compression desalination system: An exergo-economic approach," Energy, Elsevier, vol. 140(P1), pages 1107-1120.
    12. 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.
    13. Mohammad Eslamian & Ali Abkar, 2014. "Viscosity iterative scheme for generalized mixed equilibrium problems and nonexpansive semigroups," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 554-570, July.
    14. F. Cianciaruso & G. Marino & L. Muglia, 2010. "Iterative Methods for Equilibrium and Fixed Point Problems for Nonexpansive Semigroups in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 491-509, August.
    15. Atid Kangtunyakarn, 2013. "A new iterative scheme for fixed point problems of infinite family of κ i -pseudo contractive mappings, equilibrium problem, variational inequality problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1543-1562, August.
    16. Wachirapong Jirakitpuwapat & Poom Kumam & Yeol Je Cho & Kanokwan Sitthithakerngkiet, 2019. "A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing," Mathematics, MDPI, vol. 7(3), pages 1-20, February.
    17. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    18. S. Saeidi & D. S. Kim, 2014. "Combination of the Hybrid Steepest-Descent Method and the Viscosity Approximation," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 911-930, March.
    19. Vahid Darvish, 2016. "Strong convergence theorem for a system of generalized mixed equilibrium problems and finite family of Bregman nonexpansive mappings in Banach spaces," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 584-603, September.
    20. Abkar, A. & Tavakkoli, M., 2015. "A new algorithm for two finite families of demicontractive mappings and equilibrium problems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 491-500.

    More about this item

    Keywords

    convex minimization problem; $CAT(0)$ spaces; resolvent identity; asymptotically quasi-nonexpansive mapping; proximal point algorithm;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    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:ibn:jmrjnl:v:10:y:2018:i:2:p:66. 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: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    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.