Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations

Boubakeur Benahmed (), Hocine Mokhtar-Kharroubi (), Bruno Malafosse () and Adnan Yassine ()

Journal of Global Optimization, 2011, vol. 49, issue 3, 365-379

Abstract: In the first part of this paper, we give a survey on convergence rates analysis of quasi-Newton methods in infinite Hilbert spaces for nonlinear equations. Then, in the second part we apply quasi-Newton methods in their Hilbert formulation to solve matrix equations. So, we prove, under natural assumptions, that quasi-Newton methods converge locally and superlinearly; the global convergence is also studied. For numerical calculations, we propose new formulations of these methods based on the matrix representation of the dyadic operator and the vectorization of matrices. Finally, we apply our results to algebraic Riccati equations. Copyright Springer Science+Business Media, LLC. 2011

Keywords: Nonlinear equations; Optimization problems; Quasi-Newton methods; Rate of convergence; Linear convergence; Superlinear convergence; Hilbert space; Matrix equations; Algebraic Riccati equation (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10898-010-9564-2 (text/html)
Access to full text is restricted to subscribers.

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:jglopt:v:49:y:2011:i:3:p:365-379

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-010-9564-2

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

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