Efficiently solving total least squares with Tikhonov identical regularization

Meijia Yang (), Yong Xia (), Jiulin Wang () and Jiming Peng ()
Additional contact information
Meijia Yang: Beihang University
Yong Xia: Beihang University
Jiulin Wang: Beihang University
Jiming Peng: University of Houston

Computational Optimization and Applications, 2018, vol. 70, issue 2, No 9, 592 pages

Abstract: Abstract The Tikhonov identical regularized total least squares (TI) is to deal with the ill-conditioned system of linear equations where the data are contaminated by noise. A standard approach for (TI) is to reformulate it as a problem of finding a zero point of some decreasing concave non-smooth univariate function such that the classical bisection search and Dinkelbach’s method can be applied. In this paper, by exploring the hidden convexity of (TI), we reformulate it as a new problem of finding a zero point of a strictly decreasing, smooth and concave univariate function. This allows us to apply the classical Newton’s method to the reformulated problem, which converges globally to the unique root with an asymptotic quadratic convergence rate. Moreover, in every iteration of Newton’s method, no optimization subproblem such as the extended trust-region subproblem is needed to evaluate the new univariate function value as it has an explicit expression. Promising numerical results based on the new algorithm are reported.

Keywords: Fractional programming; Quadratic programming; Total least square; Tikhonov regularization; Bisection method; Newton’s method; Trust-region subproblem; S-lemma; 90C26; 90C20; 90C32 (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/s10589-018-0004-4 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:coopap:v:70:y:2018:i:2:d:10.1007_s10589-018-0004-4

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-018-0004-4

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

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