Superlinear convergence of nonlinear conjugate gradient method and scaled memoryless BFGS method based on assumptions about the initial point

Sarah Nataj and S.H. Lui

Applied Mathematics and Computation, 2020, vol. 369, issue C

Abstract: The Perry nonlinear conjugate gradient method and scaled memoryless BFGS method are two quasi-Newton methods for unconstrained minimization. All convergence theory in the literature assume existence of a minimizer and bounds on the objective function in a neighbourhood of the minimizer. These conditions cannot be checked in practice. The motivation of this work is to derive a convergence theory where all assumptions can be verified, and the existence of a minimizer and its superlinear rate of convergence are consequences of the theory. Only the basic versions of these methods without line search are considered. The theory is simple in the sense that it contains as few constants as possible.

Keywords: Perry nonlinear conjugate gradient; Scaled memoryless BFGS; Unconstrained optimization; Quasi-Newton method (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319308215
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:369:y:2020:i:c:s0096300319308215

DOI: 10.1016/j.amc.2019.124829

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().