Decomposition approach for the global minimization of biconcave functions over polytopes
Identifieur interne : 000F72 ( Istex/Corpus ); précédent : 000F71; suivant : 000F73Decomposition approach for the global minimization of biconcave functions over polytopes
Auteurs : R. Horst ; N. V. ThoaiSource :
- Journal of Optimization Theory and Applications [ 0022-3239 ] ; 1996-03-01.
Abstract
Abstract: A decomposition approach is proposed for minimizing biconcave functions over polytopes. Important special cases include concave minimization, bilinear and indefinite quadratic programming for which new algorithms result. The approach introduces a new polyhedral partition and combines branch-and-bound techniques, outer approximation, and projection of polytopes in a suitable way.
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DOI: 10.1007/BF02192199
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ISTEX:FFCB51FEC2582379A530BEC5EB89AFA018C24965Le document en format XML
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Horst</name><affiliation><mods:affiliation>Fachbereich IV, Department of Mathematics, University of Trier, Trier, Germany</mods:affiliation></affiliation></author><author><name sortKey="Thoai, N V" sort="Thoai, N V" uniqKey="Thoai N" first="N. V." last="Thoai">N. V. Thoai</name><affiliation><mods:affiliation>Institute of Mathematics, Hanoi, Vietnam</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Journal of Optimization Theory and Applications</title><title level="j" type="abbrev">J Optim Theory Appl</title><idno type="ISSN">0022-3239</idno><idno type="eISSN">1573-2878</idno><imprint><publisher>Kluwer Academic Publishers-Plenum Publishers</publisher><pubPlace>New York</pubPlace><date type="published" when="1996-03-01">1996-03-01</date><biblScope unit="volume">88</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="561">561</biblScope><biblScope unit="page" to="583">583</biblScope></imprint><idno type="ISSN">0022-3239</idno></series><idno type="istex">FFCB51FEC2582379A530BEC5EB89AFA018C24965</idno><idno type="DOI">10.1007/BF02192199</idno><idno type="ArticleID">BF02192199</idno><idno type="ArticleID">Art3</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0022-3239</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: A decomposition approach is proposed for minimizing biconcave functions over polytopes. Important special cases include concave minimization, bilinear and indefinite quadratic programming for which new algorithms result. The approach introduces a new polyhedral partition and combines branch-and-bound techniques, outer approximation, and projection of polytopes in a suitable way.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>R. Horst</name><affiliations><json:string>Fachbereich IV, Department of Mathematics, University of Trier, Trier, Germany</json:string></affiliations></json:item><json:item><name>N. V. 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The approach introduces a new polyhedral partition and combines branch-and-bound techniques, outer approximation, and projection of polytopes in a suitable way.</abstract><qualityIndicators><score>5.588</score><pdfVersion>1.3</pdfVersion><pdfPageSize>432 x 648 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>391</abstractCharCount><pdfWordCount>6530</pdfWordCount><pdfCharCount>28785</pdfCharCount><pdfPageCount>23</pdfPageCount><abstractWordCount>49</abstractWordCount></qualityIndicators><title>Decomposition approach for the global minimization of biconcave functions over polytopes</title><refBibs><json:item><host><author><json:item><name>Al-Khayyal </name></json:item><json:item><name>F,A </name></json:item></author><title>Constrained Bilinear Programming and Jointly Related Problems</title><publicationDate>1983</publicationDate></host></json:item><json:item><author><json:item><name>Horst </name></json:item><json:item><name>R 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</name></json:item></author><title>Canonical DC-Programming Techniques for Solving a Convex Program with an Additional Constraint of Multiplicative Type, Computing</title><publicationDate>1993</publicationDate></host></json:item><json:item><author><json:item><name>Horst </name></json:item><json:item><name>R Thoar</name></json:item><json:item><name>N,V </name></json:item></author><host><pages><last>48</last><first>39</first></pages><author></author><title>A New Algorithm for Solving the General Quadratic Problem</title><publicationDate>1990</publicationDate></host><publicationDate>1990</publicationDate></json:item><json:item><host><pages><last>289</last><first>271</first></pages><author><json:item><name>Horst </name></json:item><json:item><name>R </name></json:item><json:item><name>Thoai </name></json:item><json:item><name>N,V </name></json:item></author><title>Modification, Implementation, and Comparison of Three Algorithms for Globally Solving Linearly-Constrained Concave Minimization Problems, Computing</title><publicationDate>1989</publicationDate></host></json:item><json:item><author><json:item><name>Horst </name></json:item><json:item><name>R Thoai</name></json:item><json:item><name>N,V </name></json:item><json:item><name>Benson </name></json:item><json:item><name>H,P </name></json:item></author><host><volume>50</volume><pages><last>274</last><first>259</first></pages><author></author><title>Mathematical Programming</title><publicationDate>1991</publicationDate></host><title>Concave Minimization via Conical Partitions and Polyhedral Outer Approximation</title><publicationDate>1991</publicationDate></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>88</volume><pages><last>583</last><first>561</first></pages><issn><json:string>0022-3239</json:string></issn><issue>3</issue><subject><json:item><value>Theory of Computation</value></json:item><json:item><value>Applications of 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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>Kluwer Academic Publishers-Plenum Publishers</publisher><pubPlace>New York</pubPlace><availability><p>Plenum Publishing Corporation, 1996</p></availability><date>1996</date></publicationStmt><notesStmt><note>Contributed Papers</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Decomposition approach for the global minimization of biconcave functions over polytopes</title><author xml:id="author-1"><persName><forename type="first">R.</forename><surname>Horst</surname></persName><note type="biography">Professor</note><affiliation>Professor</affiliation><affiliation>Fachbereich IV, Department of Mathematics, University of Trier, Trier, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">N.</forename><surname>Thoai</surname></persName><note type="biography">Associate Professor</note><affiliation>Associate Professor</affiliation><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation></author></analytic><monogr><title level="j">Journal of Optimization Theory and Applications</title><title level="j" type="abbrev">J Optim Theory Appl</title><idno type="journal-ID">10957</idno><idno type="pISSN">0022-3239</idno><idno type="eISSN">1573-2878</idno><idno type="issue-article-count">16</idno><idno type="volume-issue-count">3</idno><imprint><publisher>Kluwer Academic Publishers-Plenum Publishers</publisher><pubPlace>New York</pubPlace><date type="published" when="1996-03-01"></date><biblScope unit="volume">88</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="561">561</biblScope><biblScope unit="page" to="583">583</biblScope></imprint></monogr><idno type="istex">FFCB51FEC2582379A530BEC5EB89AFA018C24965</idno><idno type="DOI">10.1007/BF02192199</idno><idno type="ArticleID">BF02192199</idno><idno type="ArticleID">Art3</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1996</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: A decomposition approach is proposed for minimizing biconcave functions over polytopes. Important special cases include concave minimization, bilinear and indefinite quadratic programming for which new algorithms result. The approach introduces a new polyhedral partition and combines branch-and-bound techniques, outer approximation, and projection of polytopes in a suitable way.</p></abstract><textClass><keywords scheme="Journal Subject"><list><head>Mathematics</head><item><term>Theory of Computation</term></item><item><term>Applications of Mathematics</term></item><item><term>Optimization</term></item><item><term>Calculus of Variations and Optimal Control</term></item><item><term>Optimization</term></item><item><term>Engineering, general</term></item><item><term>Operations Research/Decision Theory</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1996-03-01">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="2017-01-20">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/FFCB51FEC2582379A530BEC5EB89AFA018C24965/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>Kluwer Academic Publishers-Plenum Publishers</PublisherName><PublisherLocation>New York</PublisherLocation></PublisherInfo><Journal><JournalInfo JournalProductType="ArchiveJournal" 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TocLevels="0"><VolumeIDStart>88</VolumeIDStart><VolumeIDEnd>88</VolumeIDEnd><VolumeIssueCount>3</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo TocLevels="0"><IssueIDStart>3</IssueIDStart><IssueIDEnd>3</IssueIDEnd><IssueArticleCount>16</IssueArticleCount><IssueHistory><CoverDate><Year>1996</Year><Month>3</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>Plenum Publishing Corporation</CopyrightHolderName><CopyrightYear>1996</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art3"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF02192199</ArticleID><ArticleDOI>10.1007/BF02192199</ArticleDOI><ArticleSequenceNumber>3</ArticleSequenceNumber><ArticleTitle Language="En">Decomposition approach for the global minimization of biconcave functions over polytopes</ArticleTitle><ArticleCategory>Contributed Papers</ArticleCategory><ArticleFirstPage>561</ArticleFirstPage><ArticleLastPage>583</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>9</Month><Day>9</Day></RegistrationDate></ArticleHistory><ArticleCopyright><CopyrightHolderName>Plenum Publishing Corporation</CopyrightHolderName><CopyrightYear>1996</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>10957</JournalID><VolumeIDStart>88</VolumeIDStart><VolumeIDEnd>88</VolumeIDEnd><IssueIDStart>3</IssueIDStart><IssueIDEnd>3</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>R.</GivenName><FamilyName>Horst</FamilyName></AuthorName><Role>Professor</Role></Author><Author AffiliationIDS="Aff2" PresentAffiliationID="Aff1"><AuthorName DisplayOrder="Western"><GivenName>N.</GivenName><GivenName>V.</GivenName><FamilyName>Thoai</FamilyName></AuthorName><Role>Associate Professor</Role></Author><Affiliation ID="Aff1"><OrgDivision>Fachbereich IV, Department of Mathematics</OrgDivision><OrgName>University of Trier</OrgName><OrgAddress><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Institute of Mathematics</OrgName><OrgAddress><City>Hanoi</City><Country>Vietnam</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>A decomposition approach is proposed for minimizing biconcave functions over polytopes. Important special cases include concave minimization, bilinear and indefinite quadratic programming for which new algorithms result. The approach introduces a new polyhedral partition and combines branch-and-bound techniques, outer approximation, and projection of polytopes in a suitable way.</Para></Abstract><KeywordGroup Language="En"><Heading>Key Words</Heading><Keyword>Global optimization</Keyword><Keyword>biconcave programming</Keyword><Keyword>concave minimization</Keyword><Keyword>bilinear and quadratic programming</Keyword><Keyword>branch-and-bound algorithms</Keyword><Keyword>outer approximations.</Keyword></KeywordGroup><ArticleNote Type="CommunicatedBy"><SimplePara>Communicated by H. P. Benson</SimplePara></ArticleNote><ArticleNote Type="Misc"><SimplePara>The authors are indebted to two anonymous reviewers for suggestions which have considerably improved this article.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Decomposition approach for the global minimization of biconcave functions over polytopes</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Decomposition approach for the global minimization of biconcave functions over polytopes</title></titleInfo><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Horst</namePart><affiliation>Fachbereich IV, Department of Mathematics, University of Trier, Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role><description>Professor</description></name><name type="personal"><namePart type="given">N.</namePart><namePart type="given">V.</namePart><namePart type="family">Thoai</namePart><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation><role><roleTerm type="text">author</roleTerm></role><description>Associate Professor</description></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper"></genre><originInfo><publisher>Kluwer Academic Publishers-Plenum Publishers</publisher><place><placeTerm type="text">New York</placeTerm></place><dateIssued encoding="w3cdtf">1996-03-01</dateIssued><copyrightDate encoding="w3cdtf">1996</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 decomposition approach is proposed for minimizing biconcave functions over polytopes. Important special cases include concave minimization, bilinear and indefinite quadratic programming for which new algorithms result. The approach introduces a new polyhedral partition and combines branch-and-bound techniques, outer approximation, and projection of polytopes in a suitable way.</abstract><note>Contributed Papers</note><relatedItem type="host"><titleInfo><title>Journal of Optimization Theory and Applications</title></titleInfo><titleInfo type="abbreviated"><title>J Optim Theory Appl</title></titleInfo><genre type="journal" displayLabel="Archive Journal"></genre><originInfo><dateIssued encoding="w3cdtf">1996-03-01</dateIssued><copyrightDate encoding="w3cdtf">1996</copyrightDate></originInfo><subject><genre>Mathematics</genre><topic>Theory of Computation</topic><topic>Applications of Mathematics</topic><topic>Optimization</topic><topic>Calculus of Variations and Optimal Control</topic><topic>Optimization</topic><topic>Engineering, general</topic><topic>Operations Research/Decision Theory</topic></subject><identifier type="ISSN">0022-3239</identifier><identifier type="eISSN">1573-2878</identifier><identifier type="JournalID">10957</identifier><identifier type="IssueArticleCount">16</identifier><identifier type="VolumeIssueCount">3</identifier><part><date>1996</date><detail type="volume"><number>88</number><caption>vol.</caption></detail><detail type="issue"><number>3</number><caption>no.</caption></detail><extent unit="pages"><start>561</start><end>583</end></extent></part><recordInfo><recordOrigin>Plenum Publishing Corporation, 1996</recordOrigin></recordInfo></relatedItem><identifier type="istex">FFCB51FEC2582379A530BEC5EB89AFA018C24965</identifier><identifier type="DOI">10.1007/BF02192199</identifier><identifier type="ArticleID">BF02192199</identifier><identifier type="ArticleID">Art3</identifier><accessCondition type="use and reproduction" contentType="copyright">Plenum Publishing Corporation, 1996</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Plenum Publishing Corporation, 1996</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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|texte= Decomposition approach for the global minimization of biconcave functions over polytopes
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