IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v194y2022i2d10.1007_s10957-022-02044-9.html
   My bibliography  Save this article

Novel Multi-level Projected Iteration to Solve Inverse Problems with Nearly Optimal Accuracy

Author

Listed:
  • Gaurav Mittal

    (Indian Institute of Technology Roorkee)

  • Ankik Kumar Giri

    (Indian Institute of Technology Roorkee)

Abstract

In this paper, we introduce a novel nonlinear projected iterative method to solve the ill-posed inverse problems in Banach spaces. This method is motivated by the well-known iteratively regularized Landweber iteration method. We analyze the convergence of our novel method by assuming the conditional stability of the inverse problem on a convex and compact set. Further, we consider a nested family of convex and compact sets on which stability holds, and based on this family, we develop a multi-level algorithm with nearly optimal accuracy. To enhance the accuracy between neighboring levels, we couple the increase in accuracy with the growth of stability constants. This ensures that the algorithm terminates within a finite number of iterations after achieving a certain discrepancy criterion. Moreover, we discuss example of an ill-posed problem on which our both the methods are applicable and deduce various constants appearing in our work.

Suggested Citation

  • Gaurav Mittal & Ankik Kumar Giri, 2022. "Novel Multi-level Projected Iteration to Solve Inverse Problems with Nearly Optimal Accuracy," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 643-680, August.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:2:d:10.1007_s10957-022-02044-9
    DOI: 10.1007/s10957-022-02044-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-022-02044-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-022-02044-9?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. Mittal, Gaurav & Giri, Ankik Kumar, 2021. "Iteratively regularized Landweber iteration method: Convergence analysis via Hölder stability," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Y. Alber & D. Butnariu, 1997. "Convergence of Bregman Projection Methods for Solving Consistent Convex Feasibility Problems in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 33-61, 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. Fischer, Aurélie, 2010. "Quantization and clustering with Bregman divergences," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2207-2221, October.
    2. Juan Enrique Martínez-Legaz & Maryam Tamadoni Jahromi & Eskandar Naraghirad, 2022. "On Bregman-Type Distances and Their Associated Projection Mappings," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 107-117, June.
    3. M. B. Lee & S. H. Park, 2004. "Convergence of Sequential Parafirmly Nonexpansive Mappings in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 549-571, December.

    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:spr:joptap:v:194:y:2022:i:2:d:10.1007_s10957-022-02044-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.