On the convergence rate of imperfect minimization algorithms in Broyden'sβ-class View Full Text


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Article Info

DATE

1975-12

AUTHORS

Josef Stoer

ABSTRACT

This paper presents a local convergence analysis of Broyden's class of rank-2 algorithms for solving unconstrained minimization problems,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$h(\bar x) = \min h(x)$$ \end{document},h ∈ C1(Rn), assuming that the step-size ai in each iterationxi+1 =xi -αiHi▽h(xi) is determined by approximate line searches only. Many of these methods including the ones most often used in practice, converge locally at least with R-order,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\tau \geqslant \sqrt[n]{2}$$ \end{document}. More... »

PAGES

313-335

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01681353

DOI

http://dx.doi.org/10.1007/bf01681353

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1017545953


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