UnivTrevesV1, Istex, Corpus, bibRecord, 001029

Approximate quasi-Newton methods

Identifieur interne : 001029 ( Istex/Corpus ); précédent : 001028; suivant : 001030

Approximate quasi-Newton methods

Auteurs : C. T. Kelley ; E. W. Sachs

Source :

Mathematical Programming [ 0025-5610 ] ; 1990-03-01.

RBID : ISTEX:BF3E64FF371C4BB2252672C3BD5F59441F9BBED1

Abstract

Abstract: We consider the effect of approximation on performance of quasi-Newton methods for infinite dimensional problems. In particular we study methods in which the approximation is refined at each iterate. We show how the local convergence behavior of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are considered.

Url:

https://api.istex.fr/document/BF3E64FF371C4BB2252672C3BD5F59441F9BBED1/fulltext/pdf

DOI: 10.1007/BF01582251

Links to Exploration step

ISTEX:BF3E64FF371C4BB2252672C3BD5F59441F9BBED1

Le document en format XML

<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Approximate quasi-Newton methods</title>
<author><name sortKey="Kelley, C T" sort="Kelley, C T" uniqKey="Kelley C" first="C. T." last="Kelley">C. T. Kelley</name>
<affiliation><mods:affiliation>Department of Mathematics, North Carolina State University, P.O. Box 8205, 27695-8205, Raleigh, NC, USA</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Sachs, E W" sort="Sachs, E W" uniqKey="Sachs E" first="E. W." last="Sachs">E. W. Sachs</name>
<affiliation><mods:affiliation>FB-IV Mathematik, Universität Trier, Postfach 3825, 5500, Trier, FR Germany</mods:affiliation>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:BF3E64FF371C4BB2252672C3BD5F59441F9BBED1</idno>
<date when="1990" year="1990">1990</date>
<idno type="doi">10.1007/BF01582251</idno>
<idno type="url">https://api.istex.fr/document/BF3E64FF371C4BB2252672C3BD5F59441F9BBED1/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001029</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001029</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Approximate quasi-Newton methods</title>
<author><name sortKey="Kelley, C T" sort="Kelley, C T" uniqKey="Kelley C" first="C. T." last="Kelley">C. T. Kelley</name>
<affiliation><mods:affiliation>Department of Mathematics, North Carolina State University, P.O. Box 8205, 27695-8205, Raleigh, NC, USA</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Sachs, E W" sort="Sachs, E W" uniqKey="Sachs E" first="E. W." last="Sachs">E. W. Sachs</name>
<affiliation><mods:affiliation>FB-IV Mathematik, Universität Trier, Postfach 3825, 5500, Trier, FR Germany</mods:affiliation>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Mathematical Programming</title>
<title level="j" type="abbrev">Mathematical Programming</title>
<idno type="ISSN">0025-5610</idno>
<idno type="eISSN">1436-4646</idno>
<imprint><publisher>Springer-Verlag</publisher>
<pubPlace>Berlin/Heidelberg</pubPlace>
<date type="published" when="1990-03-01">1990-03-01</date>
<biblScope unit="volume">48</biblScope>
<biblScope unit="issue">1-3</biblScope>
<biblScope unit="page" from="41">41</biblScope>
<biblScope unit="page" to="70">70</biblScope>
</imprint>
<idno type="ISSN">0025-5610</idno>
</series>
<idno type="istex">BF3E64FF371C4BB2252672C3BD5F59441F9BBED1</idno>
<idno type="DOI">10.1007/BF01582251</idno>
<idno type="ArticleID">BF01582251</idno>
<idno type="ArticleID">Art4</idno>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0025-5610</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: We consider the effect of approximation on performance of quasi-Newton methods for infinite dimensional problems. In particular we study methods in which the approximation is refined at each iterate. We show how the local convergence behavior of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are considered.</div>
</front>
</TEI>
<istex><corpusName>springer</corpusName>
<author><json:item><name>C. T. Kelley</name>
<affiliations><json:string>Department of Mathematics, North Carolina State University, P.O. Box 8205, 27695-8205, Raleigh, NC, USA</json:string>
</affiliations>
</json:item>
<json:item><name>E. W. Sachs</name>
<affiliations><json:string>FB-IV Mathematik, Universität Trier, Postfach 3825, 5500, Trier, FR Germany</json:string>
</affiliations>
</json:item>
</author>
<articleId><json:string>BF01582251</json:string>
<json:string>Art4</json:string>
</articleId>
<language><json:string>eng</json:string>
</language>
<originalGenre><json:string>OriginalPaper</json:string>
</originalGenre>
<abstract>Abstract: We consider the effect of approximation on performance of quasi-Newton methods for infinite dimensional problems. In particular we study methods in which the approximation is refined at each iterate. We show how the local convergence behavior of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are considered.</abstract>
<qualityIndicators><score>5.744</score>
<pdfVersion>1.3</pdfVersion>
<pdfPageSize>447 x 666 pts</pdfPageSize>
<refBibsNative>false</refBibsNative>
<keywordCount>0</keywordCount>
<abstractCharCount>434</abstractCharCount>
<pdfWordCount>11397</pdfWordCount>
<pdfCharCount>54388</pdfCharCount>
<pdfPageCount>30</pdfPageCount>
<abstractWordCount>62</abstractWordCount>
</qualityIndicators>
<title>Approximate quasi-Newton methods</title>
<refBibs><json:item><author><json:item><name>E,L Allgower</name>
</json:item>
<json:item><name>K B6hmer</name>
</json:item>
<json:item><name>F,A Potra</name>
</json:item>
<json:item><name>W,C Rheinboldt</name>
</json:item>
</author>
<host><volume>23</volume>
<pages><last>169</last>
<first>160</first>
</pages>
<author></author>
<title>SlAM Journal on Numerical Analysis</title>
<publicationDate>1986</publicationDate>
</host>
<title>A mesh-independence principle for operator equations and their discretizations</title>
<publicationDate>1986</publicationDate>
</json:item>
<json:item><author><json:item><name>C,G Broyden</name>
</json:item>
</author>
<host><volume>19</volume>
<pages><last>593</last>
<first>577</first>
</pages>
<author></author>
<title>Mathematics of Computation</title>
<publicationDate>1965</publicationDate>
</host>
<title>A class of methods for solving simultaneous equations</title>
<publicationDate>1965</publicationDate>
</json:item>
<json:item><author><json:item><name>C,G Broyden</name>
</json:item>
</author>
<host><volume>16</volume>
<pages><first>670</first>
</pages>
<author></author>
<title>AMS Notices</title>
<publicationDate>1969</publicationDate>
</host>
<title>A new double-rank minimization algorithm</title>
<publicationDate>1969</publicationDate>
</json:item>
<json:item><author><json:item><name>C,G Broyden</name>
</json:item>
</author>
<host><volume>24</volume>
<pages><last>382</last>
<first>365</first>
</pages>
<author></author>
<title>Mathematics" of Computation</title>
<publicationDate>1970</publicationDate>
</host>
<title>The convergence of single rank quasi-Newton methods</title>
<publicationDate>1970</publicationDate>
</json:item>
<json:item><author><json:item><name>C,G Broyden</name>
</json:item>
</author>
<host><volume>25</volume>
<pages><last>294</last>
<first>285</first>
</pages>
<author></author>
<title>Mathematics of Computation</title>
<publicationDate>1971</publicationDate>
</host>
<title>The convergence of an algorithm for solving sparse nonlinear systems</title>
<publicationDate>1971</publicationDate>
</json:item>
<json:item><author><json:item><name>C,G Broyden</name>
</json:item>
<json:item><name>J,E Dennis</name>
</json:item>
<json:item><name>J,J Mor6</name>
</json:item>
</author>
<host><volume>12</volume>
<pages><last>246</last>
<first>223</first>
</pages>
<author></author>
<title>Journal of the Institute of Mathematics and its Applications</title>
<publicationDate>1973</publicationDate>
</host>
<title>On the local and superlinear convergence of quasi- Newton methods</title>
<publicationDate>1973</publicationDate>
</json:item>
<json:item><author><json:item><name>R,S Dembo</name>
</json:item>
<json:item><name>S,C Eisenstat</name>
</json:item>
<json:item><name>T Steihaug</name>
</json:item>
</author>
<host><volume>19</volume>
<pages><last>408</last>
<first>400</first>
</pages>
<author></author>
<title>Inexact Newton methods SIAM Journal on Numerical Analysis</title>
<publicationDate>1982</publicationDate>
</host>
<publicationDate>1982</publicationDate>
</json:item>
<json:item><author><json:item><name>J,E Dennis</name>
</json:item>
<json:item><name>R,B </name>
</json:item>
</author>
<host><author></author>
<title>Numerical Methods for Nonlinear Equations and Unconstrained Optimization</title>
<publicationDate>1983</publicationDate>
</host>
<publicationDate>1983</publicationDate>
</json:item>
<json:item><author><json:item><name>J,E Dennis</name>
</json:item>
<json:item><name>H,F Walker</name>
</json:item>
</author>
<host><volume>3</volume>
<pages><last>987</last>
<first>949</first>
</pages>
<author></author>
<title>SIAM Journal on Numerical Analysis</title>
<publicationDate>1981</publicationDate>
</host>
<title>Convergence theorems for least change secant update methods</title>
<publicationDate>1981</publicationDate>
</json:item>
<json:item><author><json:item><name>J,E Dennis</name>
</json:item>
<json:item><name>H,F Walker</name>
</json:item>
</author>
<host><volume>22</volume>
<pages><last>778</last>
<first>760</first>
</pages>
<author></author>
<title>SIAM Journal on Numerical Analysis</title>
<publicationDate>1985</publicationDate>
</host>
<title>Least-change sparse secant updates with inaccurate secant conditions</title>
<publicationDate>1985</publicationDate>
</json:item>
<json:item><author><json:item><name>J,C Dunn</name>
</json:item>
</author>
<host><volume>24</volume>
<pages><last>1191</last>
<first>1177</first>
</pages>
<author></author>
<title>SIAM Journal on Control and Optimization</title>
<publicationDate>1986</publicationDate>
</host>
<title>Diagonally modified conditional gradient methods for input constrained optimal control problems</title>
<publicationDate>1986</publicationDate>
</json:item>
<json:item><author><json:item><name>J,C Dunn</name>
</json:item>
<json:item><name>E,W Sachs</name>
</json:item>
</author>
<host><volume>10</volume>
<pages><last>147</last>
<first>143</first>
</pages>
<author></author>
<title>Applied Mathematics and Optimization</title>
<publicationDate>1983</publicationDate>
</host>
<title>The effect of perturbations on the convergence rates of optimization algorithms</title>
<publicationDate>1983</publicationDate>
</json:item>
<json:item><author><json:item><name>R Fletcher</name>
</json:item>
</author>
<host><volume>13</volume>
<pages><last>322</last>
<first>317</first>
</pages>
<author></author>
<title>Computer Journal</title>
<publicationDate>1970</publicationDate>
</host>
<title>A new approach to variable metric methods</title>
<publicationDate>1970</publicationDate>
</json:item>
<json:item><author><json:item><name>Z Fortuna</name>
</json:item>
</author>
<host><volume>16</volume>
<pages><last>384</last>
<first>380</first>
</pages>
<author></author>
<title>SlAM Journal on Numerical Analysis</title>
<publicationDate>1979</publicationDate>
</host>
<title>Some convergence properties of the conjugate gradient method in Hilbert space</title>
<publicationDate>1979</publicationDate>
</json:item>
<json:item><author><json:item><name>D Goldfarb</name>
</json:item>
</author>
<host><volume>24</volume>
<pages><last>26</last>
<first>23</first>
</pages>
<author></author>
<title>Mathematics of Computation</title>
<publicationDate>1970</publicationDate>
</host>
<title>A family of variable metric methods derived by variational means</title>
<publicationDate>1970</publicationDate>
</json:item>
<json:item><author><json:item><name>A Griewank</name>
</json:item>
</author>
<host><pages><last>321</last>
<first>309</first>
</pages>
<author></author>
<title>Proceedings of CTAC</title>
<publicationDate>1985-08</publicationDate>
</host>
<title>The solution of boundary value problems by Broyden based secant methods Computational Techniques and Applications: CTAC 85</title>
<publicationDate>1985-08</publicationDate>
</json:item>
<json:item><author><json:item><name>A Griewank</name>
</json:item>
</author>
<host><volume>1230</volume>
<pages><last>157</last>
<first>138</first>
</pages>
<author></author>
<title>VoL</title>
<publicationDate>1987</publicationDate>
</host>
<title>Rates of convergence for secant methods on nonlinear problems in Hilbert space</title>
<publicationDate>1987</publicationDate>
</json:item>
<json:item><author><json:item><name>A Griewank</name>
</json:item>
</author>
<host><volume>24</volume>
<pages><last>705</last>
<first>684</first>
</pages>
<author></author>
<title>SlAM Journal on Numerical Analysis</title>
<publicationDate>1987</publicationDate>
</host>
<title>The local convergence of Broyden-like methods on Lipschitzian problems in Hilbert space</title>
<publicationDate>1987</publicationDate>
</json:item>
<json:item><author><json:item><name>A Griewank</name>
</json:item>
<json:item><name>P,L Toint</name>
</json:item>
</author>
<host><volume>39</volume>
<pages><last>137</last>
<first>119</first>
</pages>
<author></author>
<title>Numerische Mathematik</title>
<publicationDate>1982</publicationDate>
</host>
<title>Partitioned variable metric methods for large structured optimization problems</title>
<publicationDate>1982</publicationDate>
</json:item>
<json:item><author><json:item><name>R,D Grigorieff</name>
</json:item>
</author>
<host><volume>69</volume>
<pages><last>272</last>
<first>253</first>
</pages>
<author></author>
<title>Mathematische Nachrichten</title>
<publicationDate>1975</publicationDate>
</host>
<publicationDate>1975</publicationDate>
</json:item>
<json:item><author><json:item><name>W Hackbusch</name>
</json:item>
</author>
<host><author></author>
<title>Multigrid Methods for Integral and Differential Equations</title>
<publicationDate>1985</publicationDate>
</host>
<title>Multigrid methods of the second kind</title>
<publicationDate>1985</publicationDate>
</json:item>
<json:item><author><json:item><name>W,E Hart</name>
</json:item>
<json:item><name>S,O W </name>
</json:item>
</author>
<host><volume>11</volume>
<pages><last>359</last>
<first>351</first>
</pages>
<author></author>
<title>Journal of the Institute of Applied Mathematics</title>
<publicationDate>1973</publicationDate>
</host>
<title>Quasi-Newton methods for discretized nonlinear boundary problems</title>
<publicationDate>1973</publicationDate>
</json:item>
<json:item><author><json:item><name>P Henrici</name>
</json:item>
</author>
<host><author></author>
<title>Discrete Variable Methods in Ordinary Differential Equations</title>
<publicationDate>1962</publicationDate>
</host>
<publicationDate>1962</publicationDate>
</json:item>
<json:item><author><json:item><name>L,V Kantorovich</name>
</json:item>
<json:item><name>G,P Akilov</name>
</json:item>
</author>
<host><author></author>
<title>Functional Analysis in Normed Spaces</title>
<publicationDate>1964</publicationDate>
</host>
<publicationDate>1964</publicationDate>
</json:item>
<json:item><author><json:item><name>C,T Kelley</name>
</json:item>
<json:item><name>J Northrup</name>
</json:item>
</author>
<host><pages><last>180</last>
<first>167</first>
</pages>
<author></author>
<title>Distributed Parameter Systems</title>
<publicationDate>1987</publicationDate>
</host>
<title>Pointwise quasi-Newton methods and some applications</title>
<publicationDate>1987</publicationDate>
</json:item>
<json:item><author><json:item><name>C,T Kelley</name>
</json:item>
<json:item><name>J,1 Northrup</name>
</json:item>
</author>
<host><volume>25</volume>
<pages><last>1155</last>
<first>1138</first>
</pages>
<author></author>
<title>SIAM Journal on Numerical Analysis</title>
<publicationDate>1988</publicationDate>
</host>
<title>A pointwise quasi-Newton method for integral equations</title>
<publicationDate>1988</publicationDate>
</json:item>
<json:item><author><json:item><name>C,T Kelley</name>
</json:item>
<json:item><name>E,W Sachs</name>
</json:item>
</author>
<host><pages><last>44</last>
<first>25</first>
</pages>
<author></author>
<title>Journal of lntegra[ Equations</title>
<publicationDate>1985</publicationDate>
</host>
<title>Broyden's method for approximate solution of nonlinear integral equations</title>
<publicationDate>1985</publicationDate>
</json:item>
<json:item><author><json:item><name>C,T Kelley</name>
</json:item>
<json:item><name>E,W Sachs</name>
</json:item>
</author>
<host><volume>24</volume>
<pages><last>531</last>
<first>516</first>
</pages>
<author></author>
<title>SIAM Journal on Numerical Analysis</title>
<publicationDate>1987</publicationDate>
</host>
<title>A quasi-Newton method for elliptic boundary value problems</title>
<publicationDate>1987</publicationDate>
</json:item>
<json:item><author><json:item><name>C,T Kelley</name>
</json:item>
<json:item><name>E,W Sachs</name>
</json:item>
</author>
<host><volume>25</volume>
<pages><last>1517</last>
<first>1503</first>
</pages>
<author></author>
<title>SIAM Journal on Control and Optimization</title>
<publicationDate>1987</publicationDate>
</host>
<title>Quasi-Newton methods and optimal control problems</title>
<publicationDate>1987</publicationDate>
</json:item>
<json:item><author><json:item><name>C,T Kelley</name>
</json:item>
<json:item><name>E,W Sachs</name>
</json:item>
</author>
<host><volume>55</volume>
<pages><last>176</last>
<first>159</first>
</pages>
<author></author>
<title>Numerische Mathematik</title>
<publicationDate>1989</publicationDate>
</host>
<title>A pointwise quasi-Newton method for unconstrained optimal control problems</title>
<publicationDate>1989</publicationDate>
</json:item>
<json:item><author><json:item><name>R Klessig</name>
</json:item>
<json:item><name>E Polak</name>
</json:item>
</author>
<host><volume>11</volume>
<pages><last>95</last>
<first>80</first>
</pages>
<author></author>
<title>SIAM Journal on Control</title>
<publicationDate>1973</publicationDate>
</host>
<title>An adaptive precision gradient method for optimal control</title>
<publicationDate>1973</publicationDate>
</json:item>
<json:item><author><json:item><name>E,S </name>
</json:item>
</author>
<host><volume>16</volume>
<pages><last>604</last>
<first>588</first>
</pages>
<author></author>
<title>SIAM Journal on Numerical Analysis</title>
<publicationDate>1979</publicationDate>
</host>
<title>Convergence results for Schubert's method for solving sparse nonlinear equations</title>
<publicationDate>1979</publicationDate>
</json:item>
<json:item><author><json:item><name>E Sachs</name>
</json:item>
</author>
<host><volume>35</volume>
<pages><last>82</last>
<first>71</first>
</pages>
<author></author>
<title>Mathematical Programming</title>
<publicationDate>1986</publicationDate>
</host>
<title>Broyden's method in Hilbert space</title>
<publicationDate>1986</publicationDate>
</json:item>
<json:item><author><json:item><name>E,W Sachs</name>
</json:item>
</author>
<host><volume>48</volume>
<pages><last>190</last>
<first>175</first>
</pages>
<author></author>
<title>Journal of Optimization Theory and Applications</title>
<publicationDate>1986</publicationDate>
</host>
<title>Rates of convergence for adaptive Newton methods</title>
<publicationDate>1986</publicationDate>
</json:item>
<json:item><author><json:item><name>K Schittkowski</name>
</json:item>
</author>
<host><volume>17</volume>
<pages><last>98</last>
<first>82</first>
</pages>
<author></author>
<title>SIAM Journal on Control</title>
<publicationDate>1979</publicationDate>
</host>
<title>An adaptive precision method for nonlinear optimization problems</title>
<publicationDate>1979</publicationDate>
</json:item>
<json:item><author><json:item><name>L,K Schubert</name>
</json:item>
</author>
<host><volume>24</volume>
<pages><last>30</last>
<first>27</first>
</pages>
<author></author>
<title>Mathematics of Computation</title>
<publicationDate>1970</publicationDate>
</host>
<title>Modification on a quasi-Newton method for nonlinear equations with sparse Jacobian</title>
<publicationDate>1970</publicationDate>
</json:item>
<json:item><author><json:item><name>D,F Shanno</name>
</json:item>
</author>
<host><volume>24</volume>
<pages><last>657</last>
<first>647</first>
</pages>
<author></author>
<title>Mathematics of Computation</title>
<publicationDate>1970</publicationDate>
</host>
<title>Conditioning of quasi-Newton methods for function minimization</title>
<publicationDate>1970</publicationDate>
</json:item>
<json:item><author><json:item><name>A,H Sherman</name>
</json:item>
</author>
<host><volume>15</volume>
<pages><last>776</last>
<first>755</first>
</pages>
<author></author>
<title>SIAM Journal on Numerical Analysis</title>
<publicationDate>1978</publicationDate>
</host>
<title>On Newton-iterative methods for the solution of systems of nonlinear equations</title>
<publicationDate>1978</publicationDate>
</json:item>
<json:item><author><json:item><name>J Stoer</name>
</json:item>
</author>
<host><volume>28</volume>
<pages><last>52</last>
<first>37</first>
</pages>
<author></author>
<title>Linear Algebra and Applications</title>
<publicationDate>1984</publicationDate>
</host>
<title>Two examples on the convergence of certain rank-2 minimization methods for quadratic functionals in Hilbert space</title>
<publicationDate>1984</publicationDate>
</json:item>
<json:item><author><json:item><name>F </name>
</json:item>
</author>
<host><volume>190</volume>
<pages><last>92</last>
<first>45</first>
</pages>
<author></author>
<title>Mathematische Annalen</title>
<publicationDate>1979</publicationDate>
</host>
<title>Diskrete Konvergenz linearer Operatoren</title>
<publicationDate>1979</publicationDate>
</json:item>
<json:item><author><json:item><name>R,A Tapia</name>
</json:item>
</author>
<host><volume>22</volume>
<pages><last>194</last>
<first>135</first>
</pages>
<author></author>
<title>Journal of Optimization Theory and Applications</title>
<publicationDate>1977</publicationDate>
</host>
<title>Diagonalized multiplier methods and quasi-Newton methods for constrained optimization</title>
<publicationDate>1977</publicationDate>
</json:item>
<json:item><author><json:item><name>L Ph</name>
</json:item>
<json:item><name> Toint</name>
</json:item>
</author>
<host><volume>16</volume>
<pages><last>1045</last>
<first>1036</first>
</pages>
<author></author>
<title>SIAM Journal on Numerical Analysis</title>
<publicationDate>1979</publicationDate>
</host>
<title>On the superlinear convergence of an algorithm for solving a sparse minimization problem</title>
<publicationDate>1979</publicationDate>
</json:item>
</refBibs>
<genre><json:string>research-article</json:string>
</genre>
<host><volume>48</volume>
<pages><last>70</last>
<first>41</first>
</pages>
<issn><json:string>0025-5610</json:string>
</issn>
<issue>1-3</issue>
<subject><json:item><value>Mathematics of Computing</value>
</json:item>
<json:item><value>Numerical Analysis</value>
</json:item>
<json:item><value>Combinatorics</value>
</json:item>
<json:item><value>Calculus of Variations and Optimal Control</value>
</json:item>
<json:item><value>Optimization</value>
</json:item>
<json:item><value>Mathematical and Computational Physics</value>
</json:item>
<json:item><value>Mathematical Methods in Physics</value>
</json:item>
<json:item><value>Numerical and Computational Methods</value>
</json:item>
<json:item><value>Operation Research/Decision Theory</value>
</json:item>
</subject>
<journalId><json:string>10107</json:string>
</journalId>
<genre><json:string>journal</json:string>
</genre>
<language><json:string>unknown</json:string>
</language>
<eissn><json:string>1436-4646</json:string>
</eissn>
<title>Mathematical Programming</title>
<publicationDate>1990</publicationDate>
<copyrightDate>1990</copyrightDate>
</host>
<categories><wos><json:string>science</json:string>
<json:string>operations research & management science</json:string>
<json:string>mathematics, applied</json:string>
<json:string>computer science, software engineering</json:string>
</wos>
<scienceMetrix><json:string>applied sciences</json:string>
<json:string>engineering</json:string>
<json:string>operations research</json:string>
</scienceMetrix>
</categories>
<publicationDate>1990</publicationDate>
<copyrightDate>1990</copyrightDate>
<doi><json:string>10.1007/BF01582251</json:string>
</doi>
<id>BF3E64FF371C4BB2252672C3BD5F59441F9BBED1</id>
<score>0.46068078</score>
<fulltext><json:item><extension>pdf</extension>
<original>true</original>
<mimetype>application/pdf</mimetype>
<uri>https://api.istex.fr/document/BF3E64FF371C4BB2252672C3BD5F59441F9BBED1/fulltext/pdf</uri>
</json:item>
<json:item><extension>zip</extension>
<original>false</original>
<mimetype>application/zip</mimetype>
<uri>https://api.istex.fr/document/BF3E64FF371C4BB2252672C3BD5F59441F9BBED1/fulltext/zip</uri>
</json:item>
<istex:fulltextTEI uri="https://api.istex.fr/document/BF3E64FF371C4BB2252672C3BD5F59441F9BBED1/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Approximate quasi-Newton methods</title>
<respStmt><resp>Références bibliographiques récupérées via GROBID</resp>
<name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name>
</respStmt>
<respStmt><resp>Références bibliographiques récupérées via GROBID</resp>
<name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name>
</respStmt>
</titleStmt>
<publicationStmt><authority>ISTEX</authority>
<publisher>Springer-Verlag</publisher>
<pubPlace>Berlin/Heidelberg</pubPlace>
<availability><p>The Mathematical Programming Society, Inc., 1990</p>
</availability>
<date>1990</date>
</publicationStmt>
<sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Approximate quasi-Newton methods</title>
<author xml:id="author-1"><persName><forename type="first">C.</forename>
<surname>Kelley</surname>
</persName>
<affiliation>Department of Mathematics, North Carolina State University, P.O. Box 8205, 27695-8205, Raleigh, NC, USA</affiliation>
</author>
<author xml:id="author-2"><persName><forename type="first">E.</forename>
<surname>Sachs</surname>
</persName>
<affiliation>FB-IV Mathematik, Universität Trier, Postfach 3825, 5500, Trier, FR Germany</affiliation>
</author>
</analytic>
<monogr><title level="j">Mathematical Programming</title>
<title level="j" type="abbrev">Mathematical Programming</title>
<idno type="journal-ID">10107</idno>
<idno type="pISSN">0025-5610</idno>
<idno type="eISSN">1436-4646</idno>
<idno type="issue-article-count">21</idno>
<idno type="volume-issue-count">3</idno>
<imprint><publisher>Springer-Verlag</publisher>
<pubPlace>Berlin/Heidelberg</pubPlace>
<date type="published" when="1990-03-01"></date>
<biblScope unit="volume">48</biblScope>
<biblScope unit="issue">1-3</biblScope>
<biblScope unit="page" from="41">41</biblScope>
<biblScope unit="page" to="70">70</biblScope>
</imprint>
</monogr>
<idno type="istex">BF3E64FF371C4BB2252672C3BD5F59441F9BBED1</idno>
<idno type="DOI">10.1007/BF01582251</idno>
<idno type="ArticleID">BF01582251</idno>
<idno type="ArticleID">Art4</idno>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><creation><date>1990</date>
</creation>
<langUsage><language ident="en">en</language>
</langUsage>
<abstract xml:lang="en"><p>Abstract: We consider the effect of approximation on performance of quasi-Newton methods for infinite dimensional problems. In particular we study methods in which the approximation is refined at each iterate. We show how the local convergence behavior of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are considered.</p>
</abstract>
<textClass><classCode scheme="AMS(MOS) Subject Classifications">45D15</classCode>
<classCode scheme="AMS(MOS) Subject Classifications">65H10</classCode>
</textClass>
<textClass><keywords scheme="Journal Subject"><list><head>Mathematics</head>
<item><term>Mathematics of Computing</term>
</item>
<item><term>Numerical Analysis</term>
</item>
<item><term>Combinatorics</term>
</item>
<item><term>Calculus of Variations and Optimal Control</term>
</item>
<item><term>Optimization</term>
</item>
<item><term>Mathematical and Computational Physics</term>
</item>
<item><term>Mathematical Methods in Physics</term>
</item>
<item><term>Numerical and Computational Methods</term>
</item>
<item><term>Operation Research/Decision Theory</term>
</item>
</list>
</keywords>
</textClass>
</profileDesc>
<revisionDesc><change when="1990-03-01">Published</change>
<change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-22">References added</change>
<change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-21">References added</change>
</revisionDesc>
</teiHeader>
</istex:fulltextTEI>
<json:item><extension>txt</extension>
<original>false</original>
<mimetype>text/plain</mimetype>
<uri>https://api.istex.fr/document/BF3E64FF371C4BB2252672C3BD5F59441F9BBED1/fulltext/txt</uri>
</json:item>
</fulltext>
<metadata><istex:metadataXml wicri:clean="Springer, Publisher found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration>
<istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType>
<istex:document><Publisher><PublisherInfo><PublisherName>Springer-Verlag</PublisherName>
<PublisherLocation>Berlin/Heidelberg</PublisherLocation>
</PublisherInfo>
<Journal><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>10107</JournalID>
<JournalPrintISSN>0025-5610</JournalPrintISSN>
<JournalElectronicISSN>1436-4646</JournalElectronicISSN>
<JournalTitle>Mathematical Programming</JournalTitle>
<JournalAbbreviatedTitle>Mathematical Programming</JournalAbbreviatedTitle>
<JournalSubjectGroup><JournalSubject Type="Primary">Mathematics</JournalSubject>
<JournalSubject Type="Secondary">Mathematics of Computing</JournalSubject>
<JournalSubject Type="Secondary">Numerical Analysis</JournalSubject>
<JournalSubject Type="Secondary">Combinatorics</JournalSubject>
<JournalSubject Type="Secondary">Calculus of Variations and Optimal Control</JournalSubject>
<JournalSubject Type="Secondary">Optimization</JournalSubject>
<JournalSubject Type="Secondary">Mathematical and Computational Physics</JournalSubject>
<JournalSubject Type="Secondary">Mathematical Methods in Physics</JournalSubject>
<JournalSubject Type="Secondary">Numerical and Computational Methods</JournalSubject>
<JournalSubject Type="Secondary">Operation Research/Decision Theory</JournalSubject>
</JournalSubjectGroup>
</JournalInfo>
<Volume><VolumeInfo VolumeType="Regular" TocLevels="0"><VolumeIDStart>48</VolumeIDStart>
<VolumeIDEnd>48</VolumeIDEnd>
<VolumeIssueCount>3</VolumeIssueCount>
</VolumeInfo>
<Issue IssueType="Combined"><IssueInfo TocLevels="0"><IssueIDStart>1</IssueIDStart>
<IssueIDEnd>3</IssueIDEnd>
<IssueArticleCount>21</IssueArticleCount>
<IssueHistory><CoverDate><Year>1990</Year>
<Month>3</Month>
</CoverDate>
</IssueHistory>
<IssueCopyright><CopyrightHolderName>The Mathematical Programming Society, Inc.</CopyrightHolderName>
<CopyrightYear>1990</CopyrightYear>
</IssueCopyright>
</IssueInfo>
<Article ID="Art4"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF01582251</ArticleID>
<ArticleDOI>10.1007/BF01582251</ArticleDOI>
<ArticleSequenceNumber>4</ArticleSequenceNumber>
<ArticleTitle Language="En">Approximate quasi-Newton methods</ArticleTitle>
<ArticleFirstPage>41</ArticleFirstPage>
<ArticleLastPage>70</ArticleLastPage>
<ArticleHistory><RegistrationDate><Year>2005</Year>
<Month>4</Month>
<Day>14</Day>
</RegistrationDate>
</ArticleHistory>
<ArticleCopyright><CopyrightHolderName>The Mathematical Programming Society, Inc.</CopyrightHolderName>
<CopyrightYear>1990</CopyrightYear>
</ArticleCopyright>
<ArticleGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant>
<AbstractGrant Grant="OpenAccess"></AbstractGrant>
<BodyPDFGrant Grant="Restricted"></BodyPDFGrant>
<BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant>
<BibliographyGrant Grant="Restricted"></BibliographyGrant>
<ESMGrant Grant="Restricted"></ESMGrant>
</ArticleGrants>
<ArticleContext><JournalID>10107</JournalID>
<VolumeIDStart>48</VolumeIDStart>
<VolumeIDEnd>48</VolumeIDEnd>
<IssueIDStart>1</IssueIDStart>
<IssueIDEnd>3</IssueIDEnd>
</ArticleContext>
</ArticleInfo>
<ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>C.</GivenName>
<GivenName>T.</GivenName>
<FamilyName>Kelley</FamilyName>
</AuthorName>
</Author>
<Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>E.</GivenName>
<GivenName>W.</GivenName>
<FamilyName>Sachs</FamilyName>
</AuthorName>
</Author>
<Affiliation ID="Aff1"><OrgDivision>Department of Mathematics</OrgDivision>
<OrgName>North Carolina State University</OrgName>
<OrgAddress><Postbox>P.O. Box 8205</Postbox>
<Postcode>27695-8205</Postcode>
<City>Raleigh</City>
<State>NC</State>
<Country>USA</Country>
</OrgAddress>
</Affiliation>
<Affiliation ID="Aff2"><OrgDivision>FB-IV Mathematik</OrgDivision>
<OrgName>Universität Trier</OrgName>
<OrgAddress><Postbox>Postfach 3825</Postbox>
<Postcode>5500</Postcode>
<City>Trier</City>
<Country>FR Germany</Country>
</OrgAddress>
</Affiliation>
</AuthorGroup>
<Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading>
<Para>We consider the effect of approximation on performance of quasi-Newton methods for infinite dimensional problems. In particular we study methods in which the approximation is refined at each iterate. We show how the local convergence behavior of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are considered.</Para>
</Abstract>
<KeywordGroup Language="En"><Heading>AMS(MOS) Subject Classifications</Heading>
<Keyword>45D15</Keyword>
<Keyword>65H10</Keyword>
</KeywordGroup>
<KeywordGroup Language="En"><Heading>Key words</Heading>
<Keyword>Quasi-Newton methods</Keyword>
<Keyword>interpolation</Keyword>
<Keyword>boundary value problems</Keyword>
<Keyword>integral equations</Keyword>
</KeywordGroup>
<ArticleNote Type="Misc"><SimplePara>The research of this author was supported by NSF grant DMS-8601139 and AFOSR grant AFOSR-ISSA-860074.</SimplePara>
</ArticleNote>
</ArticleHeader>
<NoBody></NoBody>
</Article>
</Issue>
</Volume>
</Journal>
</Publisher>
</istex:document>
</istex:metadataXml>
<mods version="3.6"><titleInfo lang="en"><title>Approximate quasi-Newton methods</title>
</titleInfo>
<titleInfo type="alternative" contentType="CDATA" lang="en"><title>Approximate quasi-Newton methods</title>
</titleInfo>
<name type="personal"><namePart type="given">C.</namePart>
<namePart type="given">T.</namePart>
<namePart type="family">Kelley</namePart>
<affiliation>Department of Mathematics, North Carolina State University, P.O. Box 8205, 27695-8205, Raleigh, NC, USA</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">E.</namePart>
<namePart type="given">W.</namePart>
<namePart type="family">Sachs</namePart>
<affiliation>FB-IV Mathematik, Universität Trier, Postfach 3825, 5500, Trier, FR Germany</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<typeOfResource>text</typeOfResource>
<genre type="research-article" displayLabel="OriginalPaper"></genre>
<originInfo><publisher>Springer-Verlag</publisher>
<place><placeTerm type="text">Berlin/Heidelberg</placeTerm>
</place>
<dateIssued encoding="w3cdtf">1990-03-01</dateIssued>
<copyrightDate encoding="w3cdtf">1990</copyrightDate>
</originInfo>
<language><languageTerm type="code" authority="rfc3066">en</languageTerm>
<languageTerm type="code" authority="iso639-2b">eng</languageTerm>
</language>
<physicalDescription><internetMediaType>text/html</internetMediaType>
</physicalDescription>
<abstract lang="en">Abstract: We consider the effect of approximation on performance of quasi-Newton methods for infinite dimensional problems. In particular we study methods in which the approximation is refined at each iterate. We show how the local convergence behavior of the quasi-Newton method in the infinite dimensional setting is affected by the refinement strategy. Applications to boundary value problems and integral equations are considered.</abstract>
<classification displayLabel="AMS(MOS) Subject Classifications">45D15</classification>
<classification displayLabel="AMS(MOS) Subject Classifications">65H10</classification>
<relatedItem type="host"><titleInfo><title>Mathematical Programming</title>
</titleInfo>
<titleInfo type="abbreviated"><title>Mathematical Programming</title>
</titleInfo>
<genre type="journal" displayLabel="Archive Journal"></genre>
<originInfo><dateIssued encoding="w3cdtf">1990-03-01</dateIssued>
<copyrightDate encoding="w3cdtf">1990</copyrightDate>
</originInfo>
<subject><genre>Mathematics</genre>
<topic>Mathematics of Computing</topic>
<topic>Numerical Analysis</topic>
<topic>Combinatorics</topic>
<topic>Calculus of Variations and Optimal Control</topic>
<topic>Optimization</topic>
<topic>Mathematical and Computational Physics</topic>
<topic>Mathematical Methods in Physics</topic>
<topic>Numerical and Computational Methods</topic>
<topic>Operation Research/Decision Theory</topic>
</subject>
<identifier type="ISSN">0025-5610</identifier>
<identifier type="eISSN">1436-4646</identifier>
<identifier type="JournalID">10107</identifier>
<identifier type="IssueArticleCount">21</identifier>
<identifier type="VolumeIssueCount">3</identifier>
<part><date>1990</date>
<detail type="volume"><number>48</number>
<caption>vol.</caption>
</detail>
<detail type="issue"><number>1-3</number>
<caption>no.</caption>
</detail>
<extent unit="pages"><start>41</start>
<end>70</end>
</extent>
</part>
<recordInfo><recordOrigin>The Mathematical Programming Society, Inc., 1990</recordOrigin>
</recordInfo>
</relatedItem>
<identifier type="istex">BF3E64FF371C4BB2252672C3BD5F59441F9BBED1</identifier>
<identifier type="DOI">10.1007/BF01582251</identifier>
<identifier type="ArticleID">BF01582251</identifier>
<identifier type="ArticleID">Art4</identifier>
<accessCondition type="use and reproduction" contentType="copyright">The Mathematical Programming Society, Inc., 1990</accessCondition>
<recordInfo><recordContentSource>SPRINGER</recordContentSource>
<recordOrigin>The Mathematical Programming Society, Inc., 1990</recordOrigin>
</recordInfo>
</mods>
</metadata>
<serie></serie>
</istex>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/Istex/Corpus

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001029 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 001029 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Rhénanie
   |area=    UnivTrevesV1
   |flux=    Istex
   |étape=   Corpus
   |type=    RBID
   |clé=     ISTEX:BF3E64FF371C4BB2252672C3BD5F59441F9BBED1
   |texte=   Approximate quasi-Newton methods
}}

This area was generated with Dilib version V0.6.31.
Data generation: Sat Jul 22 16:29:01 2017. Site generation: Wed Feb 28 14:55:37 2024

	Serveur d'exploration sur l'Université de Trèves
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur l'Université de Trèves

Approximate quasi-Newton methods

Approximate quasi-Newton methods

Source :

Abstract

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri