Convergence of algorithms for perturbed optimization problems
Identifieur interne : 001188 ( Istex/Corpus ); précédent : 001187; suivant : 001189Convergence of algorithms for perturbed optimization problems
Auteurs : Ekkehard W. SachsSource :
- Annals of Operations Research [ 0254-5330 ] ; 1990-12-01.
Abstract
Abstract: Infinite-dimensional optimization problems occur in various applications such as optimal control problems and parameter identification problems. If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints.
Url:
DOI: 10.1007/BF02055200
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ISTEX:F10280A81B4F593EA7F1B81403DC2C1BBAE59897Le document en format XML
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If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Ekkehard W. Sachs</name><affiliations><json:string>Fachbereich IV-Mathematik, Universität Trier, Postfach 3825, D-5500, Trier, Germany</json:string></affiliations></json:item></author><articleId><json:string>BF02055200</json:string><json:string>Art14</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Infinite-dimensional optimization problems occur in various applications such as optimal control problems and parameter identification problems. If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints.</abstract><qualityIndicators><score>6.164</score><pdfVersion>1.3</pdfVersion><pdfPageSize>468 x 705.28 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>694</abstractCharCount><pdfWordCount>9306</pdfWordCount><pdfCharCount>44019</pdfCharCount><pdfPageCount>31</pdfPageCount><abstractWordCount>97</abstractWordCount></qualityIndicators><title>Convergence of algorithms for perturbed optimization problems</title><refBibs><json:item><author><json:item><name>E,L Allgower</name></json:item><json:item><name>K B~shmer</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>SIAM J. 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Control Optim</title><publicationDate>1987</publicationDate></host><title>Quasi-Newton methods and unconstrained 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>Numer. Math</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>C,T Kelley</name></json:item><json:item><name>E,W Sachs</name></json:item></author><host><volume>48</volume><pages><last>70</last><first>41</first></pages><author></author><title>Math. 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Progr</title><publicationDate>1974</publicationDate></host><title>Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear programming algorithms</title><publicationDate>1974</publicationDate></json:item><json:item><author><json:item><name>E Sachs</name></json:item></author><host><volume>11</volume><pages><last>276</last><first>247</first></pages><author></author><title>Appl. Math. Optim</title><publicationDate>1984</publicationDate></host><title>Newton's method for singular constrained optimization problems</title><publicationDate>1984</publicationDate></json:item><json:item><author><json:item><name>E Sachs</name></json:item></author><host><volume>48</volume><pages><last>190</last><first>175</first></pages><author></author><title>J. Optim. Theory Appl</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>E Sachs</name></json:item></author><host><volume>35</volume><pages><last>82</last><first>71</first></pages><author></author><title>Math. Progr</title><publicationDate>1986</publicationDate></host><title>Broyden's method in Hilbert space</title><publicationDate>1986</publicationDate></json:item><json:item><host><author><json:item><name>R Winther</name></json:item></author><title>A numerical Galerkin method for a parabolic problem</title><publicationDate>1977</publicationDate></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>27</volume><pages><last>341</last><first>311</first></pages><issn><json:string>0254-5330</json:string></issn><issue>1</issue><subject><json:item><value>Theory of Computation</value></json:item><json:item><value>Combinatorics</value></json:item><json:item><value>Operations Research/Decision Theory</value></json:item></subject><journalId><json:string>10479</json:string></journalId><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1572-9338</json:string></eissn><title>Annals of Operations Research</title><publicationDate>1990</publicationDate><copyrightDate>1990</copyrightDate></host><categories><wos><json:string>science</json:string><json:string>operations research & management science</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/BF02055200</json:string></doi><id>F10280A81B4F593EA7F1B81403DC2C1BBAE59897</id><score>0.6321506</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/F10280A81B4F593EA7F1B81403DC2C1BBAE59897/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/F10280A81B4F593EA7F1B81403DC2C1BBAE59897/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/F10280A81B4F593EA7F1B81403DC2C1BBAE59897/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Convergence of algorithms for perturbed optimization problems</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>Baltzer Science Publishers, Baarn/Kluwer Academic Publishers</publisher><pubPlace>Dordrecht</pubPlace><availability><p>J.C. 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Scientific Publishing Company, 1990</p></availability><date>1990</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Convergence of algorithms for perturbed optimization problems</title><author xml:id="author-1"><persName><forename type="first">Ekkehard</forename><surname>Sachs</surname></persName><affiliation>Fachbereich IV-Mathematik, Universität Trier, Postfach 3825, D-5500, Trier, Germany</affiliation></author></analytic><monogr><title level="j">Annals of Operations Research</title><title level="j" type="abbrev">Ann Oper Res</title><idno type="journal-ID">10479</idno><idno type="pISSN">0254-5330</idno><idno type="eISSN">1572-9338</idno><idno type="issue-article-count">17</idno><idno type="volume-issue-count">0</idno><imprint><publisher>Baltzer Science Publishers, Baarn/Kluwer Academic Publishers</publisher><pubPlace>Dordrecht</pubPlace><date type="published" when="1990-12-01"></date><biblScope unit="volume">27</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="311">311</biblScope><biblScope unit="page" to="341">341</biblScope></imprint></monogr><idno type="istex">F10280A81B4F593EA7F1B81403DC2C1BBAE59897</idno><idno type="DOI">10.1007/BF02055200</idno><idno type="ArticleID">BF02055200</idno><idno type="ArticleID">Art14</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1990</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: Infinite-dimensional optimization problems occur in various applications such as optimal control problems and parameter identification problems. If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints.</p></abstract><textClass><keywords scheme="Journal Subject"><list><head>Economics / Management Science</head><item><term>Theory of Computation</term></item><item><term>Combinatorics</term></item><item><term>Operations Research/Decision Theory</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1990-12-01">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/F10280A81B4F593EA7F1B81403DC2C1BBAE59897/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>Baltzer Science Publishers, Baarn/Kluwer Academic Publishers</PublisherName><PublisherLocation>Dordrecht</PublisherLocation></PublisherInfo><Journal><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>10479</JournalID><JournalPrintISSN>0254-5330</JournalPrintISSN><JournalElectronicISSN>1572-9338</JournalElectronicISSN><JournalTitle>Annals of Operations Research</JournalTitle><JournalAbbreviatedTitle>Ann Oper Res</JournalAbbreviatedTitle><JournalSubjectGroup><JournalSubject Type="Primary">Economics / Management Science</JournalSubject><JournalSubject Type="Secondary">Theory of Computation</JournalSubject><JournalSubject Type="Secondary">Combinatorics</JournalSubject><JournalSubject Type="Secondary">Operations Research/Decision Theory</JournalSubject></JournalSubjectGroup></JournalInfo><Volume><VolumeInfo VolumeType="Regular" TocLevels="0"><VolumeIDStart>27</VolumeIDStart><VolumeIDEnd>27</VolumeIDEnd><VolumeIssueCount>0</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo TocLevels="0"><IssueIDStart>1</IssueIDStart><IssueIDEnd>1</IssueIDEnd><IssueArticleCount>17</IssueArticleCount><IssueHistory><CoverDate><DateString>1990</DateString><Year>1990</Year><Month>12</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>J.C. Baltzer AG, Scientific Publishing Company</CopyrightHolderName><CopyrightYear>1990</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art14"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF02055200</ArticleID><ArticleDOI>10.1007/BF02055200</ArticleDOI><ArticleSequenceNumber>14</ArticleSequenceNumber><ArticleTitle Language="En">Convergence of algorithms for perturbed optimization problems</ArticleTitle><ArticleSubCategory>Part III General Algorithmic Results</ArticleSubCategory><ArticleFirstPage>311</ArticleFirstPage><ArticleLastPage>341</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>7</Month><Day>23</Day></RegistrationDate></ArticleHistory><ArticleCopyright><CopyrightHolderName>J.C. Baltzer A.G. Scientific Publishing Company</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>10479</JournalID><VolumeIDStart>27</VolumeIDStart><VolumeIDEnd>27</VolumeIDEnd><IssueIDStart>1</IssueIDStart><IssueIDEnd>1</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Ekkehard</GivenName><GivenName>W.</GivenName><FamilyName>Sachs</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgDivision>Fachbereich IV-Mathematik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><Postbox>Postfach 3825</Postbox><Postcode>D-5500</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Infinite-dimensional optimization problems occur in various applications such as optimal control problems and parameter identification problems. If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints.</Para></Abstract></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Convergence of algorithms for perturbed optimization problems</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Convergence of algorithms for perturbed optimization problems</title></titleInfo><name type="personal"><namePart type="given">Ekkehard</namePart><namePart type="given">W.</namePart><namePart type="family">Sachs</namePart><affiliation>Fachbereich IV-Mathematik, Universität Trier, Postfach 3825, D-5500, Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper"></genre><originInfo><publisher>Baltzer Science Publishers, Baarn/Kluwer Academic Publishers</publisher><place><placeTerm type="text">Dordrecht</placeTerm></place><dateIssued encoding="w3cdtf">1990-12-01</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: Infinite-dimensional optimization problems occur in various applications such as optimal control problems and parameter identification problems. If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints.</abstract><relatedItem type="host"><titleInfo><title>Annals of Operations Research</title></titleInfo><titleInfo type="abbreviated"><title>Ann Oper Res</title></titleInfo><genre type="journal" displayLabel="Archive Journal"></genre><originInfo><dateIssued encoding="w3cdtf">1990-12-01</dateIssued><copyrightDate encoding="w3cdtf">1990</copyrightDate></originInfo><subject><genre>Economics / Management Science</genre><topic>Theory of Computation</topic><topic>Combinatorics</topic><topic>Operations Research/Decision Theory</topic></subject><identifier type="ISSN">0254-5330</identifier><identifier type="eISSN">1572-9338</identifier><identifier type="JournalID">10479</identifier><identifier type="IssueArticleCount">17</identifier><identifier type="VolumeIssueCount">0</identifier><part><date>1990</date><detail type="volume"><number>27</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="pages"><start>311</start><end>341</end></extent></part><recordInfo><recordOrigin>J.C. Baltzer AG, Scientific Publishing Company, 1990</recordOrigin></recordInfo></relatedItem><identifier type="istex">F10280A81B4F593EA7F1B81403DC2C1BBAE59897</identifier><identifier type="DOI">10.1007/BF02055200</identifier><identifier type="ArticleID">BF02055200</identifier><identifier type="ArticleID">Art14</identifier><accessCondition type="use and reproduction" contentType="copyright">J.C. Baltzer A.G. Scientific Publishing Company, 1990</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>J.C. Baltzer A.G. Scientific Publishing Company, 1990</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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