On the relation between quadratic termination and convergence properties of minimization algorithms View Full Text


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Article Info

DATE

1977-09

AUTHORS

J. Stoer

ABSTRACT

Many algorithms for solving minimization problems of the form\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathop {\min }\limits_{x \in R^n } f(x) = f(\bar x),f:R^n \to R,$$ \end{document} are devised such that they terminate with the optimal solution\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar x$$ \end{document} within at mostn steps, when applied to the minimization of strictly convex quadratic functionsf onRn. In this paper general conditions are given, which together with the quadratic termination property, will ensure that the algorithm locally converges at leastn-step quadratically to a local minimum\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar x$$ \end{document} for sufficiently smooth nonquadratic functionsf. These conditions apply to most algorithms with the quadratic termination property. More... »

PAGES

343-366

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01389973

DOI

http://dx.doi.org/10.1007/bf01389973

DIMENSIONS

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