On the accelerating property of an algorithm for function minimization without calculating derivatives

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Abstract

It is shown that the alogrithm of Ref. E1, when converging on a uniformly convex function and when technical condition (13) of Ref. E1 is satisfied, has an n-iteration Q-superlinear rate of convergence and a behaviour which is a precursor of every-iteration Q-superlinearity. This result overrides and corrects main result Theorem 3.1 of Ref. E1. © 1978 Plenum Publishing Corporation.
Original languageEnglish
Pages (from-to)465-467
Number of pages3
JournalJournal of Optimization Theory and Applications.
Volume26
Issue number4
DOIs
Publication statusPublished - 1 Nov 1978

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Function Minimization
Derivatives
Iteration
Derivative
Uniformly Convex
Precursor
Convex function
Rate of Convergence
Theorem
Rate of convergence

Cite this

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title = "On the accelerating property of an algorithm for function minimization without calculating derivatives",
abstract = "It is shown that the alogrithm of Ref. E1, when converging on a uniformly convex function and when technical condition (13) of Ref. E1 is satisfied, has an n-iteration Q-superlinear rate of convergence and a behaviour which is a precursor of every-iteration Q-superlinearity. This result overrides and corrects main result Theorem 3.1 of Ref. E1. {\circledC} 1978 Plenum Publishing Corporation.",
author = "Frank Callier and Philippe Toint",
note = "Copyright 2007 Elsevier B.V., All rights reserved.",
year = "1978",
month = "11",
day = "1",
doi = "10.1007/BF00933468",
language = "English",
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N2 - It is shown that the alogrithm of Ref. E1, when converging on a uniformly convex function and when technical condition (13) of Ref. E1 is satisfied, has an n-iteration Q-superlinear rate of convergence and a behaviour which is a precursor of every-iteration Q-superlinearity. This result overrides and corrects main result Theorem 3.1 of Ref. E1. © 1978 Plenum Publishing Corporation.

AB - It is shown that the alogrithm of Ref. E1, when converging on a uniformly convex function and when technical condition (13) of Ref. E1 is satisfied, has an n-iteration Q-superlinear rate of convergence and a behaviour which is a precursor of every-iteration Q-superlinearity. This result overrides and corrects main result Theorem 3.1 of Ref. E1. © 1978 Plenum Publishing Corporation.

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