IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v235y2014i1p17-27.html
   My bibliography  Save this article

A viscosity method with no spectral radius requirements for the split common fixed point problem

Author

Listed:
  • Maingé, Paul-Emile

Abstract

This paper is concerned with an algorithmic solution to the split common fixed point problem in Hilbert spaces. Our method can be regarded as a variant of the “viscosity approximation method”. Under very classical assumptions, we establish a strong convergence theorem with regard to involved operators belonging to the wide class of quasi-nonexpansive operators. In contrast with other related processes, our algorithm does not require any estimate of some spectral radius. The technique of analysis developed in this work is new and can be applied to many other fixed point iterations. Numerical experiments are also performed with regard to an inverse heat problem.

Suggested Citation

  • Maingé, Paul-Emile, 2014. "A viscosity method with no spectral radius requirements for the split common fixed point problem," European Journal of Operational Research, Elsevier, vol. 235(1), pages 17-27.
  • Handle: RePEc:eee:ejores:v:235:y:2014:i:1:p:17-27
    DOI: 10.1016/j.ejor.2013.11.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713009454
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2013.11.028?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 1996. "Conditional subgradient optimization -- Theory and applications," European Journal of Operational Research, Elsevier, vol. 88(2), pages 382-403, January.
    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. Yaohua Hu & Carisa Kwok Wai Yu & Xiaoqi Yang, 2019. "Incremental quasi-subgradient methods for minimizing the sum of quasi-convex functions," Journal of Global Optimization, Springer, vol. 75(4), pages 1003-1028, December.
    2. Fei Han & Jian Wang & Lingli Huang & Yan Li & Liu He, 2023. "Modeling Impacts of Implementation Policies of Tradable Credit Schemes on Traffic Congestion in the Context of Traveler’s Cognitive Illusion," Sustainability, MDPI, vol. 15(15), pages 1-18, July.
    3. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    4. Li, Hongyan & Hendry, Linda & Teunter, Ruud, 2009. "A strategic capacity allocation model for a complex supply chain: Formulation and solution approach comparison," International Journal of Production Economics, Elsevier, vol. 121(2), pages 505-518, October.
    5. Hishinuma, Kazuhiro & Iiduka, Hideaki, 2020. "Fixed point quasiconvex subgradient method," European Journal of Operational Research, Elsevier, vol. 282(2), pages 428-437.
    6. Lisa Göransson & Caroline Granfeldt & Ann-Brith Strömberg, 2021. "Management of Wind Power Variations in Electricity System Investment Models," SN Operations Research Forum, Springer, vol. 2(2), pages 1-30, June.
    7. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 2003. "On the convergence of conditional [var epsilon]-subgradient methods for convex programs and convex-concave saddle-point problems," European Journal of Operational Research, Elsevier, vol. 151(3), pages 461-473, December.
    8. Dirk Lorenz & Marc Pfetsch & Andreas Tillmann, 2014. "An infeasible-point subgradient method using adaptive approximate projections," Computational Optimization and Applications, Springer, vol. 57(2), pages 271-306, March.
    9. K. C. Kiwiel, 1998. "Subgradient Method with Entropic Projections for Convex Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 159-173, January.
    10. Narciso, Marcelo G. & Lorena, Luiz Antonio N., 1999. "Lagrangean/surrogate relaxation for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 114(1), pages 165-177, April.
    11. Lorena, Luiz Antonio N. & Goncalves Narciso, Marcelo, 2002. "Using logical surrogate information in Lagrangean relaxation: An application to symmetric traveling salesman problems," European Journal of Operational Research, Elsevier, vol. 138(3), pages 473-483, May.
    12. Yaohua Hu & Jiawen Li & Carisa Kwok Wai Yu, 2020. "Convergence rates of subgradient methods for quasi-convex optimization problems," Computational Optimization and Applications, Springer, vol. 77(1), pages 183-212, September.
    13. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, June.
    14. Noriyoshi Sukegawa & Yoshitsugu Yamamoto & Liyuan Zhang, 2013. "Lagrangian relaxation and pegging test for the clique partitioning problem," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(4), pages 363-391, December.
    15. Hu, Yaohua & Yang, Xiaoqi & Sim, Chee-Khian, 2015. "Inexact subgradient methods for quasi-convex optimization problems," European Journal of Operational Research, Elsevier, vol. 240(2), pages 315-327.

    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:eee:ejores:v:235:y:2014:i:1:p:17-27. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.