On solving general reverse convex programming problems by a sequence of linear programs and line searches
Identifieur interne : 001055 ( Istex/Corpus ); précédent : 001054; suivant : 001056On solving general reverse convex programming problems by a sequence of linear programs and line searches
Auteurs : Reiner Horst ; Thai Q. Phong ; Nguyen V. ThoaiSource :
- Annals of Operations Research [ 0254-5330 ] ; 1990-12-01.
Abstract
Abstract: Many multiextremal global optimization problems can be formulated as problems of minimizing a linear function over the intersection of a convex set with the complement of a convex set (so-called canonical d.c. programs or general reverse convex programming problems). In this paper it is shown that these general reverse convex programming problems can be solved by a sequence of linear programs and univariate convex minimization problems (line searches).
Url:
DOI: 10.1007/BF02283684
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Thoai</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:4B64E793AF4CBA58E561967C6A629D346901EBCF</idno><date when="1990" year="1990">1990</date><idno type="doi">10.1007/BF02283684</idno><idno type="url">https://api.istex.fr/document/4B64E793AF4CBA58E561967C6A629D346901EBCF/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001055</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001055</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">On solving general reverse convex programming problems by a sequence of linear programs and line searches</title><author><name sortKey="Horst, Reiner" sort="Horst, Reiner" uniqKey="Horst R" first="Reiner" last="Horst">Reiner Horst</name><affiliation><mods:affiliation>Universität Trier, Trier, F.R. Germany</mods:affiliation></affiliation></author><author><name sortKey="Phong, Thai Q" sort="Phong, Thai Q" uniqKey="Phong T" first="Thai Q." last="Phong">Thai Q. Phong</name><affiliation><mods:affiliation>Institute of Mathematics, Hanoi, Vietnam</mods:affiliation></affiliation></author><author><name sortKey="Thoai, Nguyen V" sort="Thoai, Nguyen V" uniqKey="Thoai N" first="Nguyen V." last="Thoai">Nguyen V. Thoai</name></author></analytic><monogr></monogr><series><title level="j">Annals of Operations Research</title><title level="j" type="abbrev">Ann Oper Res</title><idno type="ISSN">0254-5330</idno><idno type="eISSN">1572-9338</idno><imprint><publisher>Baltzer Science Publishers, Baarn/Kluwer Academic Publishers</publisher><pubPlace>Dordrecht</pubPlace><date type="published" when="1990-12-01">1990-12-01</date><biblScope unit="volume">25</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="17">17</biblScope></imprint><idno type="ISSN">0254-5330</idno></series><idno type="istex">4B64E793AF4CBA58E561967C6A629D346901EBCF</idno><idno type="DOI">10.1007/BF02283684</idno><idno type="ArticleID">BF02283684</idno><idno type="ArticleID">Art2</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0254-5330</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Many multiextremal global optimization problems can be formulated as problems of minimizing a linear function over the intersection of a convex set with the complement of a convex set (so-called canonical d.c. programs or general reverse convex programming problems). 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Baltzer A.G. Scientific Publishing Company, 1990</p></availability><date>1990</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">On solving general reverse convex programming problems by a sequence of linear programs and line searches</title><author xml:id="author-1"><persName><forename type="first">Reiner</forename><surname>Horst</surname></persName><affiliation>Universität Trier, Trier, F.R. Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">Thai</forename><surname>Phong</surname></persName><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation></author><author xml:id="author-3"><persName><forename type="first">Nguyen</forename><surname>Thoai</surname></persName></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">19</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">25</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="1">1</biblScope><biblScope unit="page" to="17">17</biblScope></imprint></monogr><idno type="istex">4B64E793AF4CBA58E561967C6A629D346901EBCF</idno><idno type="DOI">10.1007/BF02283684</idno><idno type="ArticleID">BF02283684</idno><idno type="ArticleID">Art2</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1990</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: Many multiextremal global optimization problems can be formulated as problems of minimizing a linear function over the intersection of a convex set with the complement of a convex set (so-called canonical d.c. programs or general reverse convex programming problems). In this paper it is shown that these general reverse convex programming problems can be solved by a sequence of linear programs and univariate convex minimization problems (line searches).</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="2017-01-20">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/4B64E793AF4CBA58E561967C6A629D346901EBCF/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>25</VolumeIDStart><VolumeIDEnd>25</VolumeIDEnd><VolumeIssueCount>0</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo TocLevels="0"><IssueIDStart>1</IssueIDStart><IssueIDEnd>1</IssueIDEnd><IssueArticleCount>19</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="Art2"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF02283684</ArticleID><ArticleDOI>10.1007/BF02283684</ArticleDOI><ArticleSequenceNumber>2</ArticleSequenceNumber><ArticleTitle Language="En">On solving general reverse convex programming problems by a sequence of linear programs and line searches</ArticleTitle><ArticleFirstPage>1</ArticleFirstPage><ArticleLastPage>17</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>12</Month><Day>6</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>25</VolumeIDStart><VolumeIDEnd>25</VolumeIDEnd><IssueIDStart>1</IssueIDStart><IssueIDEnd>1</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Reiner</GivenName><FamilyName>Horst</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Thai</GivenName><GivenName>Q.</GivenName><FamilyName>Phong</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>Nguyen</GivenName><GivenName>V.</GivenName><FamilyName>Thoai</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgName>Universität Trier</OrgName><OrgAddress><City>Trier</City><Country>F.R. 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>Many multiextremal global optimization problems can be formulated as problems of minimizing a linear function over the intersection of a convex set with the complement of a convex set (so-called canonical d.c. programs or general reverse convex programming problems). In this paper it is shown that these general reverse convex programming problems can be solved by a sequence of linear programs and univariate convex minimization problems (line searches).</Para></Abstract><ArticleNote Type="Misc"><SimplePara>Parts of the present paper were accomplished while this author was on leave at the University of Trier as a fellow of the Alexander von Humboldt foundation.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On solving general reverse convex programming problems by a sequence of linear programs and line searches</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>On solving general reverse convex programming problems by a sequence of linear programs and line searches</title></titleInfo><name type="personal"><namePart type="given">Reiner</namePart><namePart type="family">Horst</namePart><affiliation>Universität Trier, Trier, F.R. Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Thai</namePart><namePart type="given">Q.</namePart><namePart type="family">Phong</namePart><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Nguyen</namePart><namePart type="given">V.</namePart><namePart type="family">Thoai</namePart><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: Many multiextremal global optimization problems can be formulated as problems of minimizing a linear function over the intersection of a convex set with the complement of a convex set (so-called canonical d.c. programs or general reverse convex programming problems). In this paper it is shown that these general reverse convex programming problems can be solved by a sequence of linear programs and univariate convex minimization problems (line searches).</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">19</identifier><identifier type="VolumeIssueCount">0</identifier><part><date>1990</date><detail type="volume"><number>25</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="pages"><start>1</start><end>17</end></extent></part><recordInfo><recordOrigin>J.C. 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