On R-linear convergence analysis for a class of gradient methods

Na Huang ()
Additional contact information
Na Huang: China Agricultural University

Computational Optimization and Applications, 2022, vol. 81, issue 1, No 6, 177 pages

Abstract: Abstract Gradient method is a simple optimization approach using minus gradient of the objective function as a search direction. Its efficiency highly relies on the choices of the stepsize. In this paper, the convergence behavior of a class of gradient methods, where the stepsize has an important property introduced in (Dai in Optimization 52:395–415, 2003), is analyzed. Our analysis is focused on minimization on strictly convex quadratic functions. We establish the R-linear convergence and derive an estimate for the R-factor. Specifically, if the stepsize can be expressed as a collection of Rayleigh quotient of the inverse Hessian matrix, we are able to show that these methods converge R-linearly and their R-factors are bounded above by $$1-\frac{1}{\varkappa }$$ 1 - 1 ϰ , where $$\varkappa$$ ϰ is the associated condition number. Preliminary numerical results demonstrate the tightness of our estimate of the R-factor.

Keywords: Quadratic optimization; Gradient methods; Spectral algorithms; R-linear convergence analysis; R-factor; 65K05; 90C06; 90C30 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-021-00333-z 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:81:y:2022:i:1:d:10.1007_s10589-021-00333-z

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

DOI: 10.1007/s10589-021-00333-z

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 ().