Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems
Identifieur interne : 001047 ( Istex/Corpus ); précédent : 001046; suivant : 001048Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems
Auteurs : R. Horst ; N. V. ThoaiSource :
- Computing [ 0010-485X ] ; 1989-06-01.
Abstract
Abstract: Several (theoretical) methods have been proposed for solving concave minimization problems; very little has been done on numerical issues. In this paper, three promising approaches (Cone-Splitting, Polyhedral Annexation and Outer Approximation) are considerably modified in order to enhance efficiency. Furthermore, a report is given on implementation, test and comparison on more than 100 examples with up to 50 variables and 30 linear constraints (plus nonnegativity conditions).
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DOI: 10.1007/BF02239754
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Box 631, Hanoi, Vietnam</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:F522B21095463255F11D3C5FC10D6ADAAB485F5C</idno><date when="1989" year="1989">1989</date><idno type="doi">10.1007/BF02239754</idno><idno type="url">https://api.istex.fr/document/F522B21095463255F11D3C5FC10D6ADAAB485F5C/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001047</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001047</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems</title><author><name sortKey="Horst, R" sort="Horst, R" uniqKey="Horst R" first="R." last="Horst">R. Horst</name><affiliation><mods:affiliation>Fachbereich IV, Mathematik, Universität Trier, Postfach 3825, D-5500, Trier, Federal Republic of 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>VIEN TOAN HOC Institute of Mathematics, Bò Ho, P. O. 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In this paper, three promising approaches (Cone-Splitting, Polyhedral Annexation and Outer Approximation) are considerably modified in order to enhance efficiency. Furthermore, a report is given on implementation, test and comparison on more than 100 examples with up to 50 variables and 30 linear constraints (plus nonnegativity conditions).</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Prof. Dr. R. Horst</name><affiliations><json:string>Fachbereich IV, Mathematik, Universität Trier, Postfach 3825, D-5500, Trier, Federal Republic of Germany</json:string></affiliations></json:item><json:item><name>Dr. habil N. V. Thoai</name><affiliations><json:string>VIEN TOAN HOC Institute of Mathematics, Bò Ho, P. O. 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Furthermore, a report is given on implementation, test and comparison on more than 100 examples with up to 50 variables and 30 linear constraints (plus nonnegativity conditions).</abstract><qualityIndicators><score>5.804</score><pdfVersion>1.3</pdfVersion><pdfPageSize>453.28 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>491</abstractCharCount><pdfWordCount>6712</pdfWordCount><pdfCharCount>32152</pdfCharCount><pdfPageCount>19</pdfPageCount><abstractWordCount>67</abstractWordCount></qualityIndicators><title>Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems</title><refBibs><json:item><host><pages><last>540097</last><first>1</first></pages><author><json:item><name>Sol </name></json:item></author><title>012074 (> -2.644843) Tuy-cut to the normed</title></host></json:item><json:item><host><author></author><title>O57364 x2 +O.231930x3 +O.O55175 x4 +O.573113 xs > l Tuy-cut to the original polytope: 1</title></host></json:item><json:item><host><pages><last>928723</last><first>2</first></pages><author></author><title>An (exact) optimal solution was found after 8 iterations including 2 restarts</title></host></json:item><json:item><author><json:item><name>J Falk</name></json:item><json:item><name>K,R Hoffman</name></json:item></author><host><volume>1</volume><pages><last>252</last><first>251</first></pages><author></author><title>Mathematics of Operations Research</title><publicationDate>1976</publicationDate></host><title>A successive underestimation method for concave minimization problems</title><publicationDate>1976</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>10</volume><pages><last>321</last><first>312</first></pages><author></author><title>Mathematical Programming</title><publicationDate>1976</publicationDate></host><title>An algorithm for nonconvex programming problems</title><publicationDate>1976</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>6</volume><pages><last>205</last><first>195</first></pages><author></author><title>Operations Research Spektrum</title><publicationDate>1984</publicationDate></host><title>On the global minimization of concave functions: introduction and survey</title><publicationDate>1984</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>51</volume><pages><last>291</last><first>271</first></pages><author></author><title>J. 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Theory and Appl</title><publicationDate>1986</publicationDate></host><title>A general class of branch-and-bound Methods in Global optimization with some new approaches for concave minimization</title><publicationDate>1986</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item><json:item><name>N,V Thoai</name></json:item><json:item><name>H,P Benson</name></json:item></author><host><author></author><title>Discussion Paper No. 140</title><publicationDate>1988</publicationDate></host><title>Concave minimization via conical partitions and polyhedral outer approximation</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item><json:item><name>N,V Thoai</name></json:item><json:item><name>H Tuy</name></json:item></author><host><volume>93</volume><pages><last>159</last><first>153</first></pages><author></author><title>Operations Research Spektrum</title><publicationDate>1987</publicationDate></host><title>Outer approximation by polyhedral convex sets</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item><json:item><name>N,V Thoai</name></json:item><json:item><name>J De Vries</name></json:item></author><host><volume>7</volume><pages><last>90</last><first>85</first></pages><author></author><title>Operations Research Letters</title><publicationDate>1988</publicationDate></host><title>On finding new vertices and redundant constraints in cutting plane algorithms for global optimization</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>P,M Pardalos</name></json:item><json:item><name>J,B Rosen</name></json:item></author><host><volume>28</volume><pages><last>379</last><first>367</first></pages><author></author><title>SIAM Review</title><publicationDate>1986</publicationDate></host><title>Methods for global concave minimization: a bibliographic survey</title><publicationDate>1986</publicationDate></json:item><json:item><author><json:item><name>P,M Pardalos</name></json:item><json:item><name>J,B Rosen</name></json:item></author><host><volume>268</volume><author></author><title>Lecture Notes on Computer Science</title><publicationDate>1987</publicationDate></host><title>Constrained global optimization: algorithms and applications</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>T,V Thieu</name></json:item><json:item><name>B,T Tam</name></json:item><json:item><name>V,T Ban</name></json:item></author><host><volume>8</volume><pages><last>40</last><first>21</first></pages><author></author><title>Acta Mathematica Vietnamica</title><publicationDate>1983</publicationDate></host><title>An outer approximation method for globally minimizing a concave function over a compact convex set</title><publicationDate>1983</publicationDate></json:item><json:item><author><json:item><name>N,V Thoai</name></json:item><json:item><name>H Tuy</name></json:item></author><host><volume>5</volume><pages><last>566</last><first>556</first></pages><author></author><title>Mathematics of Oper. Res</title><publicationDate>1980</publicationDate></host><title>Convergent algorithms for minimizing a concave function</title><publicationDate>1980</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item></author><host><volume>5</volume><pages><last>1440</last><first>1437</first></pages><author></author><title>Soviet Mathematics</title><publicationDate>1964</publicationDate></host><title>Concave programming under linear constraints</title><publicationDate>1964</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item></author><host><author></author><title>Preprint, Institut of Mathematics</title><publicationDate>1988</publicationDate></host><title>Normal conical algorithm for concave minimization over polytopes</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item></author><host><author></author><title>Preprint, Institute of Mathematics</title><publicationDate>1988</publicationDate></host><title>On a polyhedral annexation method for concave minimization</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item><json:item><name>R Horst</name></json:item></author><host><volume>41</volume><pages><last>183</last><first>161</first></pages><author></author><title>Mathematical Programming</title></host><title>Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization</title></json:item><json:item><author><json:item><name>H Tuy</name></json:item><json:item><name>V Khachaturov</name></json:item><json:item><name>S Utkin</name></json:item></author><host><volume>18</volume><pages><last>808</last><first>791</first></pages><author></author><title>Optimization</title><publicationDate>1987</publicationDate></host><title>A class of exhaustive cone splitting procedures in conical algorithms for concave minimization</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name> Prof</name></json:item><json:item><name> Dr</name></json:item><json:item><name> Reiner Horst</name></json:item><json:item><name>Iv Fachbereich</name></json:item><json:item><name>Mathematik Universitfit Trier</name></json:item><json:item><name>Germany Postfach 3825 D-5500 Trier Federal Republic Of</name></json:item><json:item><name>N V Dr</name></json:item><json:item><name>Vien Thoai</name></json:item><json:item><name> Toan</name></json:item><json:item><name>P Institute Of Mathematics</name></json:item></author><host><author></author><title>A-1040 Wien. --Hersteller: Satz: Austro-Filmsatz Richard Gerin</title></host><title>Box 631, B6 Ho Hanoi Vietnam Verleger: Springer-Verlag KG, M61kerbastei 5, A-1010 Wien</title></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>42</volume><pages><last>289</last><first>271</first></pages><issn><json:string>0010-485X</json:string></issn><issue>2-3</issue><subject><json:item><value>Computational Mathematics and Numerical Analysis</value></json:item></subject><journalId><json:string>607</json:string></journalId><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1436-5057</json:string></eissn><title>Computing</title><publicationDate>1989</publicationDate><copyrightDate>1989</copyrightDate></host><categories><wos><json:string>science</json:string><json:string>computer science, theory & methods</json:string></wos><scienceMetrix><json:string>natural sciences</json:string><json:string>mathematics & statistics</json:string><json:string>numerical & computational mathematics</json:string></scienceMetrix></categories><publicationDate>1989</publicationDate><copyrightDate>1989</copyrightDate><doi><json:string>10.1007/BF02239754</json:string></doi><id>F522B21095463255F11D3C5FC10D6ADAAB485F5C</id><score>0.9601254</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/F522B21095463255F11D3C5FC10D6ADAAB485F5C/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/F522B21095463255F11D3C5FC10D6ADAAB485F5C/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/F522B21095463255F11D3C5FC10D6ADAAB485F5C/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems</title><title level="a" type="alt" xml:lang="de">Modifikation, Implementierung und Vergleich dreier Algorithmen zur globalen Lösung konkaver Minimierungsprobleme mit linearen Nebenbedingungen</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>Vienna</pubPlace><availability><p>Springer-Verlag, 1989</p></availability><date>1988-08-16</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems</title><title level="a" type="alt" xml:lang="de">Modifikation, Implementierung und Vergleich dreier Algorithmen zur globalen Lösung konkaver Minimierungsprobleme mit linearen Nebenbedingungen</title><author xml:id="author-1"><persName><forename type="first">R.</forename><surname>Horst</surname></persName><roleName type="degree">Prof. Dr.</roleName><affiliation>Fachbereich IV, Mathematik, Universität Trier, Postfach 3825, D-5500, Trier, Federal Republic of Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">N.</forename><surname>Thoai</surname></persName><roleName type="degree">Dr. habil</roleName><affiliation>VIEN TOAN HOC Institute of Mathematics, Bò Ho, P. O. Box 631, Hanoi, Vietnam</affiliation></author></analytic><monogr><title level="j">Computing</title><title level="j" type="abbrev">Computing</title><idno type="journal-ID">607</idno><idno type="pISSN">0010-485X</idno><idno type="eISSN">1436-5057</idno><idno type="issue-article-count">14</idno><idno type="volume-issue-count">4</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Vienna</pubPlace><date type="published" when="1989-06-01"></date><biblScope unit="volume">42</biblScope><biblScope unit="issue">2-3</biblScope><biblScope unit="page" from="271">271</biblScope><biblScope unit="page" to="289">289</biblScope></imprint></monogr><idno type="istex">F522B21095463255F11D3C5FC10D6ADAAB485F5C</idno><idno type="DOI">10.1007/BF02239754</idno><idno type="ArticleID">BF02239754</idno><idno type="ArticleID">Art14</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1988-08-16</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: Several (theoretical) methods have been proposed for solving concave minimization problems; very little has been done on numerical issues. In this paper, three promising approaches (Cone-Splitting, Polyhedral Annexation and Outer Approximation) are considerably modified in order to enhance efficiency. Furthermore, a report is given on implementation, test and comparison on more than 100 examples with up to 50 variables and 30 linear constraints (plus nonnegativity conditions).</p></abstract><abstract xml:lang="de"><p>Zusammenfassung: Zur Lösung konkaver Minimierungsprobleme sind einige (theoretische) Verfahren vorgeschlagen worden; wenig ist über ihr numerisches Verhalten bekannt. In dieser Arbeit werden die drei Methoden „Cone-Splitting”, „Polyhedral Annexation” und „Outer Approximation” zur Steigerung ihrer Effizienz beträchtlich modifiziert. Weiters wird über Implementierung sowie Test und Vergleich an mehr als 100 Beispielen mit bis zu 50 Variablen und 30 Nebenbedingungen (plus Nichtnegativitätsbedingung) berichtet.</p></abstract><textClass><keywords scheme="Journal Subject"><list><head>Mathematics</head><item><term>Computational Mathematics and Numerical Analysis</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1988-08-16">Created</change><change when="1989-06-01">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/F522B21095463255F11D3C5FC10D6ADAAB485F5C/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>Vienna</PublisherLocation></PublisherInfo><Journal><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>607</JournalID><JournalPrintISSN>0010-485X</JournalPrintISSN><JournalElectronicISSN>1436-5057</JournalElectronicISSN><JournalTitle>Computing</JournalTitle><JournalAbbreviatedTitle>Computing</JournalAbbreviatedTitle><JournalSubjectGroup><JournalSubject Type="Primary">Mathematics</JournalSubject><JournalSubject Type="Secondary">Computational Mathematics and Numerical Analysis</JournalSubject></JournalSubjectGroup></JournalInfo><Volume><VolumeInfo VolumeType="Regular" TocLevels="0"><VolumeIDStart>42</VolumeIDStart><VolumeIDEnd>42</VolumeIDEnd><VolumeIssueCount>4</VolumeIssueCount></VolumeInfo><Issue IssueType="Combined"><IssueInfo TocLevels="0"><IssueIDStart>2</IssueIDStart><IssueIDEnd>3</IssueIDEnd><IssueArticleCount>14</IssueArticleCount><IssueHistory><CoverDate><DateString>1989</DateString><Year>1989</Year><Month>6</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1989</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art14"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF02239754</ArticleID><ArticleDOI>10.1007/BF02239754</ArticleDOI><ArticleSequenceNumber>14</ArticleSequenceNumber><ArticleTitle Language="En">Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems</ArticleTitle><ArticleTitle Language="De">Modifikation, Implementierung und Vergleich dreier Algorithmen zur globalen Lösung konkaver Minimierungsprobleme mit linearen Nebenbedingungen</ArticleTitle><ArticleFirstPage>271</ArticleFirstPage><ArticleLastPage>289</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>10</Month><Day>18</Day></RegistrationDate><Received><Year>1988</Year><Month>8</Month><Day>16</Day></Received><Revised><Year>1989</Year><Month>4</Month><Day>24</Day></Revised></ArticleHistory><ArticleCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1989</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>607</JournalID><VolumeIDStart>42</VolumeIDStart><VolumeIDEnd>42</VolumeIDEnd><IssueIDStart>2</IssueIDStart><IssueIDEnd>3</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><Prefix>Prof. Dr.</Prefix><GivenName>R.</GivenName><FamilyName>Horst</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><Prefix>Dr. habil</Prefix><GivenName>N.</GivenName><GivenName>V.</GivenName><FamilyName>Thoai</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>Federal Republic of Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>VIEN TOAN HOC Institute of Mathematics</OrgName><OrgAddress><Street>Bò Ho</Street><Postbox>P. O. Box 631</Postbox><City>Hanoi</City><Country>Vietnam</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Several (theoretical) methods have been proposed for solving concave minimization problems; very little has been done on numerical issues. In this paper, three promising approaches (Cone-Splitting, Polyhedral Annexation and Outer Approximation) are considerably modified in order to enhance efficiency. Furthermore, a report is given on implementation, test and comparison on more than 100 examples with up to 50 variables and 30 linear constraints (plus nonnegativity conditions).</Para></Abstract><Abstract ID="Abs2" Language="De"><Heading>Zusammenfassung</Heading><Para>Zur Lösung konkaver Minimierungsprobleme sind einige (theoretische) Verfahren vorgeschlagen worden; wenig ist über ihr numerisches Verhalten bekannt. In dieser Arbeit werden die drei Methoden „Cone-Splitting”, „Polyhedral Annexation” und „Outer Approximation” zur Steigerung ihrer Effizienz beträchtlich modifiziert. Weiters wird über Implementierung sowie Test und Vergleich an mehr als 100 Beispielen mit bis zu 50 Variablen und 30 Nebenbedingungen (plus Nichtnegativitätsbedingung) berichtet.</Para></Abstract><KeywordGroup Language="En"><Heading>AMS Subject Classificaiton</Heading><Keyword>90C30</Keyword></KeywordGroup><KeywordGroup Language="En"><Heading>Key words</Heading><Keyword>Constrained global optimization</Keyword><Keyword>concave minimization</Keyword></KeywordGroup><ArticleNote Type="Misc"><SimplePara>This paper was accomplished while the second author was on leave with the Alexander von Humboldt-Foundation at the University of Trier.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems</title></titleInfo><titleInfo lang="de"><title>Modifikation, Implementierung und Vergleich dreier Algorithmen zur globalen Lösung konkaver Minimierungsprobleme mit linearen Nebenbedingungen</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="de"><title>Modifikation, Implementierung und Vergleich dreier Algorithmen zur globalen Lösung konkaver Minimierungsprobleme mit linearen Nebenbedingungen</title></titleInfo><name type="personal"><namePart type="termsOfAddress">Prof. Dr.</namePart><namePart type="given">R.</namePart><namePart type="family">Horst</namePart><affiliation>Fachbereich IV, Mathematik, Universität Trier, Postfach 3825, D-5500, Trier, Federal Republic of Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="termsOfAddress">Dr. habil</namePart><namePart type="given">N.</namePart><namePart type="given">V.</namePart><namePart type="family">Thoai</namePart><affiliation>VIEN TOAN HOC Institute of Mathematics, Bò Ho, P. O. Box 631, Hanoi, Vietnam</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">Vienna</placeTerm></place><dateCreated encoding="w3cdtf">1988-08-16</dateCreated><dateIssued encoding="w3cdtf">1989-06-01</dateIssued><copyrightDate encoding="w3cdtf">1989</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: Several (theoretical) methods have been proposed for solving concave minimization problems; very little has been done on numerical issues. In this paper, three promising approaches (Cone-Splitting, Polyhedral Annexation and Outer Approximation) are considerably modified in order to enhance efficiency. Furthermore, a report is given on implementation, test and comparison on more than 100 examples with up to 50 variables and 30 linear constraints (plus nonnegativity conditions).</abstract><abstract lang="de">Zusammenfassung: Zur Lösung konkaver Minimierungsprobleme sind einige (theoretische) Verfahren vorgeschlagen worden; wenig ist über ihr numerisches Verhalten bekannt. In dieser Arbeit werden die drei Methoden „Cone-Splitting”, „Polyhedral Annexation” und „Outer Approximation” zur Steigerung ihrer Effizienz beträchtlich modifiziert. Weiters wird über Implementierung sowie Test und Vergleich an mehr als 100 Beispielen mit bis zu 50 Variablen und 30 Nebenbedingungen (plus Nichtnegativitätsbedingung) berichtet.</abstract><relatedItem type="host"><titleInfo><title>Computing</title></titleInfo><titleInfo type="abbreviated"><title>Computing</title></titleInfo><genre type="journal" displayLabel="Archive Journal"></genre><originInfo><dateIssued encoding="w3cdtf">1989-06-01</dateIssued><copyrightDate encoding="w3cdtf">1989</copyrightDate></originInfo><subject><genre>Mathematics</genre><topic>Computational Mathematics and Numerical Analysis</topic></subject><identifier type="ISSN">0010-485X</identifier><identifier type="eISSN">1436-5057</identifier><identifier type="JournalID">607</identifier><identifier type="IssueArticleCount">14</identifier><identifier type="VolumeIssueCount">4</identifier><part><date>1989</date><detail type="volume"><number>42</number><caption>vol.</caption></detail><detail type="issue"><number>2-3</number><caption>no.</caption></detail><extent unit="pages"><start>271</start><end>289</end></extent></part><recordInfo><recordOrigin>Springer-Verlag, 1989</recordOrigin></recordInfo></relatedItem><identifier type="istex">F522B21095463255F11D3C5FC10D6ADAAB485F5C</identifier><identifier type="DOI">10.1007/BF02239754</identifier><identifier type="ArticleID">BF02239754</identifier><identifier type="ArticleID">Art14</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1989</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Springer-Verlag, 1989</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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