Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and D.C. Optimization problems
Identifieur interne : 001118 ( Istex/Corpus ); précédent : 001117; suivant : 001119Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and D.C. Optimization problems
Auteurs : Hoang Tuy ; Reiner HorstSource :
- Mathematical Programming [ 0025-5610 ] ; 1988-05-01.
Abstract
Abstract: A general branch-and-bound conceptual scheme for global optimization is presented that includes along with previous branch-and-bound approaches also grid-search techniques. The corresponding convergence theory, as well as the question of restart capability for branch-and-bound algorithms used in decomposition or outer approximation schemes are discussed. As an illustration of this conceptual scheme, a finite branch-and-bound algorithm for concave minimization is described and a convergent branch-and-bound algorithm, based on the previous one, is developed for the minimization of a difference of two convex functions.
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DOI: 10.1007/BF01580762
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ISTEX:C731794D402FA8E04BD7E6EA71AAFF865C54118ALe document en format XML
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Optimization problems</title><author><name sortKey="Tuy, Hoang" sort="Tuy, Hoang" uniqKey="Tuy H" first="Hoang" last="Tuy">Hoang Tuy</name><affiliation><mods:affiliation>Institute of Mathematics, Hanoi, Vietnam</mods:affiliation></affiliation></author><author><name sortKey="Horst, Reiner" sort="Horst, Reiner" uniqKey="Horst R" first="Reiner" last="Horst">Reiner Horst</name><affiliation><mods:affiliation>Universität Trier, 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="1988-05-01">1988-05-01</date><biblScope unit="volume">41</biblScope><biblScope unit="issue">1-3</biblScope><biblScope unit="page" from="161">161</biblScope><biblScope unit="page" to="183">183</biblScope></imprint><idno type="ISSN">0025-5610</idno></series><idno type="istex">C731794D402FA8E04BD7E6EA71AAFF865C54118A</idno><idno type="DOI">10.1007/BF01580762</idno><idno type="ArticleID">BF01580762</idno><idno type="ArticleID">Art12</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: A general branch-and-bound conceptual scheme for global optimization is presented that includes along with previous branch-and-bound approaches also grid-search techniques. The corresponding convergence theory, as well as the question of restart capability for branch-and-bound algorithms used in decomposition or outer approximation schemes are discussed. As an illustration of this conceptual scheme, a finite branch-and-bound algorithm for concave minimization is described and a convergent branch-and-bound algorithm, based on the previous one, is developed for the minimization of a difference of two convex functions.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Hoang Tuy</name><affiliations><json:string>Institute of Mathematics, Hanoi, Vietnam</json:string></affiliations></json:item><json:item><name>Reiner Horst</name><affiliations><json:string>Universität Trier, Trier, FR Germany</json:string></affiliations></json:item></author><articleId><json:string>BF01580762</json:string><json:string>Art12</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: A general branch-and-bound conceptual scheme for global optimization is presented that includes along with previous branch-and-bound approaches also grid-search techniques. The corresponding convergence theory, as well as the question of restart capability for branch-and-bound algorithms used in decomposition or outer approximation schemes are discussed. As an illustration of this conceptual scheme, a finite branch-and-bound algorithm for concave minimization is described and a convergent branch-and-bound algorithm, based on the previous one, is developed for the minimization of a difference of two convex functions.</abstract><qualityIndicators><score>5.996</score><pdfVersion>1.3</pdfVersion><pdfPageSize>447 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>633</abstractCharCount><pdfWordCount>9550</pdfWordCount><pdfCharCount>42859</pdfCharCount><pdfPageCount>23</pdfPageCount><abstractWordCount>83</abstractWordCount></qualityIndicators><title>Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and D.C. 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(forthcoming)</title></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>41</volume><pages><last>183</last><first>161</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 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Application to concave minimization and D.C. 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>Springer-Verlag</publisher><pubPlace>Berlin/Heidelberg</pubPlace><availability><p>The Mathematical Programming Society, Inc., 1988</p></availability><date>1986-12-08</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and D.C. Optimization problems</title><author xml:id="author-1"><persName><forename type="first">Hoang</forename><surname>Tuy</surname></persName><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation></author><author xml:id="author-2"><persName><forename type="first">Reiner</forename><surname>Horst</surname></persName><affiliation>Universität Trier, 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">29</idno><idno type="volume-issue-count">3</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="1988-05-01"></date><biblScope unit="volume">41</biblScope><biblScope unit="issue">1-3</biblScope><biblScope unit="page" from="161">161</biblScope><biblScope unit="page" to="183">183</biblScope></imprint></monogr><idno type="istex">C731794D402FA8E04BD7E6EA71AAFF865C54118A</idno><idno type="DOI">10.1007/BF01580762</idno><idno type="ArticleID">BF01580762</idno><idno type="ArticleID">Art12</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1986-12-08</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: A general branch-and-bound conceptual scheme for global optimization is presented that includes along with previous branch-and-bound approaches also grid-search techniques. The corresponding convergence theory, as well as the question of restart capability for branch-and-bound algorithms used in decomposition or outer approximation schemes are discussed. As an illustration of this conceptual scheme, a finite branch-and-bound algorithm for concave minimization is described and a convergent branch-and-bound algorithm, based on the previous one, is developed for the minimization of a difference of two convex functions.</p></abstract><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="1986-12-08">Created</change><change when="1988-05-01">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="2017-01-20">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/C731794D402FA8E04BD7E6EA71AAFF865C54118A/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>41</VolumeIDStart><VolumeIDEnd>41</VolumeIDEnd><VolumeIssueCount>3</VolumeIssueCount></VolumeInfo><Issue IssueType="Combined"><IssueInfo TocLevels="0"><IssueIDStart>1</IssueIDStart><IssueIDEnd>3</IssueIDEnd><IssueArticleCount>29</IssueArticleCount><IssueHistory><CoverDate><Year>1988</Year><Month>5</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>The Mathematical Programming Society, Inc.</CopyrightHolderName><CopyrightYear>1988</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art12"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF01580762</ArticleID><ArticleDOI>10.1007/BF01580762</ArticleDOI><ArticleSequenceNumber>12</ArticleSequenceNumber><ArticleTitle Language="En">Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and D.C. Optimization problems</ArticleTitle><ArticleFirstPage>161</ArticleFirstPage><ArticleLastPage>183</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>4</Month><Day>13</Day></RegistrationDate><Received><Year>1986</Year><Month>12</Month><Day>8</Day></Received><Revised><Year>1987</Year><Month>11</Month><Day>30</Day></Revised></ArticleHistory><ArticleCopyright><CopyrightHolderName>The Mathematical Programming Society, Inc.</CopyrightHolderName><CopyrightYear>1988</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>41</VolumeIDStart><VolumeIDEnd>41</VolumeIDEnd><IssueIDStart>1</IssueIDStart><IssueIDEnd>3</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Hoang</GivenName><FamilyName>Tuy</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Reiner</GivenName><FamilyName>Horst</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgName>Institute of Mathematics</OrgName><OrgAddress><City>Hanoi</City><Country>Vietnam</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Universität Trier</OrgName><OrgAddress><City>Trier</City><Country>FR Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>A general branch-and-bound conceptual scheme for global optimization is presented that includes along with previous branch-and-bound approaches also grid-search techniques. The corresponding convergence theory, as well as the question of restart capability for branch-and-bound algorithms used in decomposition or outer approximation schemes are discussed. As an illustration of this conceptual scheme, a finite branch-and-bound algorithm for concave minimization is described and a convergent branch-and-bound algorithm, based on the previous one, is developed for the minimization of a difference of two convex functions.</Para></Abstract><KeywordGroup Language="En"><Heading>Key words</Heading><Keyword>Global optimization</Keyword><Keyword>nonconvex programming</Keyword><Keyword>branch-and-bound</Keyword><Keyword>restart procedure</Keyword><Keyword>decomposition</Keyword><Keyword>outer approximation</Keyword><Keyword>concave minimization</Keyword><Keyword>d.c. optimization</Keyword></KeywordGroup></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and D.C. Optimization problems</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and D.C. Optimization problems</title></titleInfo><name type="personal"><namePart type="given">Hoang</namePart><namePart type="family">Tuy</namePart><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Reiner</namePart><namePart type="family">Horst</namePart><affiliation>Universität Trier, 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><dateCreated encoding="w3cdtf">1986-12-08</dateCreated><dateIssued encoding="w3cdtf">1988-05-01</dateIssued><copyrightDate encoding="w3cdtf">1988</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: A general branch-and-bound conceptual scheme for global optimization is presented that includes along with previous branch-and-bound approaches also grid-search techniques. The corresponding convergence theory, as well as the question of restart capability for branch-and-bound algorithms used in decomposition or outer approximation schemes are discussed. As an illustration of this conceptual scheme, a finite branch-and-bound algorithm for concave minimization is described and a convergent branch-and-bound algorithm, based on the previous one, is developed for the minimization of a difference of two convex functions.</abstract><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">1988-05-01</dateIssued><copyrightDate encoding="w3cdtf">1988</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">29</identifier><identifier type="VolumeIssueCount">3</identifier><part><date>1988</date><detail type="volume"><number>41</number><caption>vol.</caption></detail><detail type="issue"><number>1-3</number><caption>no.</caption></detail><extent unit="pages"><start>161</start><end>183</end></extent></part><recordInfo><recordOrigin>The Mathematical Programming Society, Inc., 1988</recordOrigin></recordInfo></relatedItem><identifier type="istex">C731794D402FA8E04BD7E6EA71AAFF865C54118A</identifier><identifier type="DOI">10.1007/BF01580762</identifier><identifier type="ArticleID">BF01580762</identifier><identifier type="ArticleID">Art12</identifier><accessCondition type="use and reproduction" contentType="copyright">The Mathematical Programming Society, Inc., 1988</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>The Mathematical Programming Society, Inc., 1988</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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