On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems

Stefania Bellavia () and Elisa Riccietti ()
Additional contact information
Stefania Bellavia: Università di Firenze
Elisa Riccietti: Institut de Recherche en Informatique de Toulouse (IRIT)

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 3, No 7, 824-859

Abstract: Abstract In this paper, we address the stable numerical solution of ill-posed nonlinear least-squares problems with small residual. We propose an elliptical trust-region reformulation of a Levenberg–Marquardt procedure. Thanks to an appropriate choice of the trust-region radius, the proposed procedure guarantees an automatic choice of the free regularization parameters that, together with a suitable stopping criterion, ensures regularizing properties to the method. Specifically, the proposed procedure generates a sequence that even in case of noisy data has the potential to approach a solution of the unperturbed problem. The case of constrained problems is considered, too. The effectiveness of the procedure is shown on several examples of ill-posed least-squares problems.

Keywords: Ill-posed nonlinear least-squares problems; Regularization; Nonlinear stepsize control; Levenberg–Marquardt methods; Trust-region methods; 65J15; 65J20; 65K10 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1318-1 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:178:y:2018:i:3:d:10.1007_s10957-018-1318-1

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

DOI: 10.1007/s10957-018-1318-1

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 ().