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

Gaurav Mittal () and Ankik Kumar Giri ()
Additional contact information
Gaurav Mittal: Indian Institute of Technology Roorkee
Ankik Kumar Giri: Indian Institute of Technology Roorkee

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 2, No 12, 643-680

Abstract: 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.

Keywords: Nonlinear ill-posed operator equations; Inverse problems; Regularization; Iterative regularization methods; Multi-level approach; 65J22; 35R30; 47J25 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-022-02044-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:194:y:2022:i:2:d:10.1007_s10957-022-02044-9

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-022-02044-9

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().