Concave minimization via conical partitions and polyhedral outer approximation
Identifieur interne : 001040 ( Istex/Corpus ); précédent : 001039; suivant : 001041Concave minimization via conical partitions and polyhedral outer approximation
Auteurs : Reiner Horst ; Nguyen V. Thoai ; Harold P. BensonSource :
- Mathematical Programming [ 0025-5610 ] ; 1991-03-01.
Abstract
Abstract: An algorithm is proposed for globally minimizing a concave function over a compact convex set. This algorithm combines typical branch-and-bound elements like partitioning, bounding and deletion with suitably introduced cuts in such a way that the computationally most expensive subroutines of previous methods are avoided. In each step, essentially only few linear programming problems have to be solved. Some preliminary computational results are reported.
Url:
DOI: 10.1007/BF01594938
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ISTEX:3B37B634372137461C168E3123E1753159BD3187Le document en format XML
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Benson</name><affiliation><mods:affiliation>University of Florida, Gainesville, FL, USA</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:3B37B634372137461C168E3123E1753159BD3187</idno><date when="1991" year="1991">1991</date><idno type="doi">10.1007/BF01594938</idno><idno type="url">https://api.istex.fr/document/3B37B634372137461C168E3123E1753159BD3187/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001040</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001040</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Concave minimization via conical partitions and polyhedral outer approximation</title><author><name sortKey="Horst, Reiner" sort="Horst, Reiner" uniqKey="Horst R" first="Reiner" last="Horst">Reiner Horst</name><affiliation><mods:affiliation>Universitat Trier, W-5500, Trier, Germany</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><affiliation><mods:affiliation>Institute of Mathematics, Hanoi, Vietnam</mods:affiliation></affiliation></author><author><name sortKey="Benson, Harold P" sort="Benson, Harold P" uniqKey="Benson H" first="Harold P." last="Benson">Harold P. Benson</name><affiliation><mods:affiliation>University of Florida, Gainesville, FL, USA</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="1991-03-01">1991-03-01</date><biblScope unit="volume">50</biblScope><biblScope unit="issue">1-3</biblScope><biblScope unit="page" from="259">259</biblScope><biblScope unit="page" to="274">274</biblScope></imprint><idno type="ISSN">0025-5610</idno></series><idno type="istex">3B37B634372137461C168E3123E1753159BD3187</idno><idno type="DOI">10.1007/BF01594938</idno><idno type="ArticleID">BF01594938</idno><idno type="ArticleID">Art17</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: An algorithm is proposed for globally minimizing a concave function over a compact convex set. This algorithm combines typical branch-and-bound elements like partitioning, bounding and deletion with suitably introduced cuts in such a way that the computationally most expensive subroutines of previous methods are avoided. In each step, essentially only few linear programming problems have to be solved. Some preliminary computational results are reported.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Reiner Horst</name><affiliations><json:string>Universitat Trier, W-5500, Trier, Germany</json:string></affiliations></json:item><json:item><name>Nguyen V. Thoai</name><affiliations><json:string>Institute of Mathematics, Hanoi, Vietnam</json:string></affiliations></json:item><json:item><name>Harold P. Benson</name><affiliations><json:string>University of Florida, Gainesville, FL, USA</json:string></affiliations></json:item></author><articleId><json:string>BF01594938</json:string><json:string>Art17</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: An algorithm is proposed for globally minimizing a concave function over a compact convex set. This algorithm combines typical branch-and-bound elements like partitioning, bounding and deletion with suitably introduced cuts in such a way that the computationally most expensive subroutines of previous methods are avoided. In each step, essentially only few linear programming problems have to be solved. Some preliminary computational results are reported.</abstract><qualityIndicators><score>5.78</score><pdfVersion>1.3</pdfVersion><pdfPageSize>447 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>467</abstractCharCount><pdfWordCount>6517</pdfWordCount><pdfCharCount>29904</pdfCharCount><pdfPageCount>16</pdfPageCount><abstractWordCount>65</abstractWordCount></qualityIndicators><title>Concave minimization via conical partitions and polyhedral outer approximation</title><refBibs><json:item><author><json:item><name>H,P Benson</name></json:item></author><host><volume>36</volume><pages><last>134</last><first>129</first></pages><author></author><title>Journal of Optimization Theory and Applications</title><publicationDate>1982</publicationDate></host><title>On the convergence oftwo branch-and bound algorithms for nonconvex programming problems</title><publicationDate>1982</publicationDate></json:item><json:item><author><json:item><name>K,L Hoffman</name></json:item></author><host><volume>20</volume><pages><last>32</last><first>22</first></pages><author></author><title>Mathematical Programming</title><publicationDate>1981</publicationDate></host><title>A method for globally minimizing concave functions over convex sets</title><publicationDate>1981</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>19</volume><pages><last>238</last><first>237</first></pages><author></author><title>Mathematical Programming</title><publicationDate>1980</publicationDate></host><title>A note on the convergence of an algorithm for nonconvex programming problems</title><publicationDate>1980</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>Journal of Optimization Theory and Applications</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></author><host><volume>58</volume><pages><last>37</last><first>11</first></pages><author></author><title>Journal of Optimization Theory and Applications</title><publicationDate>1988</publicationDate></host><title>Deterministic global optimization with partition sets whose feasibility is not known. Application to concave minimization, d.c. programming, reverse convex constraints and Lipschitzian optimization</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>61</volume><pages><last>146</last><first>143</first></pages><author></author><title>Journal of Optimization Theory and Applications</title><publicationDate>1989</publicationDate></host><title>On consistency of bounding operations in deterministic global optimization</title><publicationDate>1989</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>37</volume><pages><last>471</last><first>433</first></pages><author></author><title>Naval Research Logistics</title><publicationDate>1990</publicationDate></host><title>Deterministic global optimization: some recent advances and new fields of applications</title><publicationDate>1990</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item><json:item><name>N,V Thoai</name></json:item></author><host><volume>58</volume><pages><last>145</last><first>139</first></pages><author></author><title>Journal of Optimization Theory and Applications</title><publicationDate>1988</publicationDate></host><title>Branch-and-bound methods for solving systems of Lipschitzian equations and inequalities</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></author><host><volume>42</volume><pages><last>289</last><first>271</first></pages><author></author><title>Computing</title><publicationDate>1989</publicationDate></host><title>Modification, implementation and comparison of three algorithms for globally solving linearly constrained concave minimization problems</title><publicationDate>1989</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>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>9</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>H Tuy</name></json:item></author><host><volume>20</volume><pages><last>264</last><first>255</first></pages><author></author><title>Optimization</title><publicationDate>1989</publicationDate></host><title>On an outer approximation concept in global optimization</title><publicationDate>1989</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item><json:item><name>H Tuy</name></json:item></author><host><volume>54</volume><pages><last>271</last><first>253</first></pages><author></author><title>Journal of Optimization Theory and Applications</title><publicationDate>1987</publicationDate></host><title>On the convergence of global methods in multi-extremal optimization</title><publicationDate>1987</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 in 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></author><host><author></author><title>Thesis (Habilitation)</title><publicationDate>1984</publicationDate></host><title>Verfahren zur LSsung konkaver Minimierungsaufgaben auf der Basis eines verallgemeinerten Erweiterungsprinzips</title><publicationDate>1984</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 Operations Research</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 Doklady</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><json:item><name>V Khatchaturov</name></json:item><json:item><name>S Utkin</name></json:item></author><host><volume>18</volume><pages><last>807</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>H Tuy</name></json:item><json:item><name>T,V Thieu</name></json:item><json:item><name>N,Q Thai</name></json:item></author><host><volume>10</volume><pages><last>514</last><first>498</first></pages><author></author><title>Mathematics of Operations Research</title><publicationDate>1985</publicationDate></host><title>A conical algorithm for globally minimizing a concave function over a closed convex set</title><publicationDate>1985</publicationDate></json:item><json:item><author><json:item><name>J. De Vries</name></json:item></author><host><author></author><title>Thesis</title><publicationDate>1986</publicationDate></host><title>Algorithmen zur konkaven Minimierung</title><publicationDate>1986</publicationDate></json:item><json:item><host><author><json:item><name>R Horst</name></json:item><json:item><name>H Tuy</name></json:item></author><title>Global Optimization -Deterministic Approaches</title><publicationDate>1990</publicationDate></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>50</volume><pages><last>274</last><first>259</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 Theory</value></json:item></subject><journalId><json:string>10107</json:string></journalId><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1436-4646</json:string></eissn><title>Mathematical Programming</title><publicationDate>1991</publicationDate><copyrightDate>1991</copyrightDate></host><categories><wos><json:string>science</json:string><json:string>operations research & management science</json:string><json:string>mathematics, applied</json:string><json:string>computer science, software engineering</json:string></wos><scienceMetrix><json:string>applied 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outer approximation</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., 1991</p></availability><date>1988-02-09</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Concave minimization via conical partitions and polyhedral outer approximation</title><author xml:id="author-1"><persName><forename type="first">Reiner</forename><surname>Horst</surname></persName><affiliation>Universitat Trier, W-5500, Trier, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">Nguyen</forename><surname>Thoai</surname></persName><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation></author><author xml:id="author-3"><persName><forename type="first">Harold</forename><surname>Benson</surname></persName><affiliation>University of Florida, Gainesville, FL, USA</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">27</idno><idno type="volume-issue-count">3</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="1991-03-01"></date><biblScope unit="volume">50</biblScope><biblScope unit="issue">1-3</biblScope><biblScope unit="page" from="259">259</biblScope><biblScope unit="page" to="274">274</biblScope></imprint></monogr><idno type="istex">3B37B634372137461C168E3123E1753159BD3187</idno><idno type="DOI">10.1007/BF01594938</idno><idno type="ArticleID">BF01594938</idno><idno type="ArticleID">Art17</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1988-02-09</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: An algorithm is proposed for globally minimizing a concave function over a compact convex set. This algorithm combines typical branch-and-bound elements like partitioning, bounding and deletion with suitably introduced cuts in such a way that the computationally most expensive subroutines of previous methods are avoided. In each step, essentially only few linear programming problems have to be solved. Some preliminary computational results are reported.</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="1988-02-09">Created</change><change when="1991-03-01">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 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TocLevels="0"><VolumeIDStart>50</VolumeIDStart><VolumeIDEnd>50</VolumeIDEnd><VolumeIssueCount>3</VolumeIssueCount></VolumeInfo><Issue IssueType="Combined"><IssueInfo TocLevels="0"><IssueIDStart>1</IssueIDStart><IssueIDEnd>3</IssueIDEnd><IssueArticleCount>27</IssueArticleCount><IssueHistory><CoverDate><Year>1991</Year><Month>3</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>The Mathematical Programming Society, Inc.</CopyrightHolderName><CopyrightYear>1991</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art17"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF01594938</ArticleID><ArticleDOI>10.1007/BF01594938</ArticleDOI><ArticleSequenceNumber>17</ArticleSequenceNumber><ArticleTitle Language="En">Concave minimization via conical partitions and polyhedral outer approximation</ArticleTitle><ArticleFirstPage>259</ArticleFirstPage><ArticleLastPage>274</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>4</Month><Day>15</Day></RegistrationDate><Received><Year>1988</Year><Month>2</Month><Day>9</Day></Received><Revised><Year>1989</Year><Month>9</Month><Day>1</Day></Revised></ArticleHistory><ArticleCopyright><CopyrightHolderName>The Mathematical Programming Society, Inc.</CopyrightHolderName><CopyrightYear>1991</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>50</VolumeIDStart><VolumeIDEnd>50</VolumeIDEnd><IssueIDStart>1</IssueIDStart><IssueIDEnd>3</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>Nguyen</GivenName><GivenName>V.</GivenName><FamilyName>Thoai</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff3"><AuthorName DisplayOrder="Western"><GivenName>Harold</GivenName><GivenName>P.</GivenName><FamilyName>Benson</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgName>Universitat Trier</OrgName><OrgAddress><Postcode>W-5500</Postcode><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><Affiliation ID="Aff3"><OrgName>University of Florida</OrgName><OrgAddress><City>Gainesville</City><State>FL</State><Country>USA</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>An algorithm is proposed for globally minimizing a concave function over a compact convex set. This algorithm combines typical branch-and-bound elements like partitioning, bounding and deletion with suitably introduced cuts in such a way that the computationally most expensive subroutines of previous methods are avoided. In each step, essentially only few linear programming problems have to be solved. Some preliminary computational results are reported.</Para></Abstract><KeywordGroup Language="En"><Heading>Key words</Heading><Keyword>Concave minimization</Keyword><Keyword>global optimization</Keyword><Keyword>nonlinear programming</Keyword><Keyword>nonconvex programming</Keyword><Keyword>branch-and-bound</Keyword><Keyword>outer approximation</Keyword><Keyword>cutting planes</Keyword></KeywordGroup><ArticleNote Type="PresentedAt"><SimplePara>Parts of the present paper were accomplished while the author was on leave at the University of Florida.</SimplePara></ArticleNote><ArticleNote Type="PresentedAt"><SimplePara>Parts of the present paper were completed while the 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>Concave minimization via conical partitions and polyhedral outer approximation</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Concave minimization via conical partitions and polyhedral outer approximation</title></titleInfo><name type="personal"><namePart type="given">Reiner</namePart><namePart type="family">Horst</namePart><affiliation>Universitat Trier, W-5500, Trier, Germany</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><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Harold</namePart><namePart type="given">P.</namePart><namePart type="family">Benson</namePart><affiliation>University of Florida, Gainesville, FL, USA</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">1988-02-09</dateCreated><dateIssued encoding="w3cdtf">1991-03-01</dateIssued><copyrightDate encoding="w3cdtf">1991</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: An algorithm is proposed for globally minimizing a concave function over a compact convex set. This algorithm combines typical branch-and-bound elements like partitioning, bounding and deletion with suitably introduced cuts in such a way that the computationally most expensive subroutines of previous methods are avoided. In each step, essentially only few linear programming problems have to be solved. Some preliminary computational results are reported.</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">1991-03-01</dateIssued><copyrightDate encoding="w3cdtf">1991</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">27</identifier><identifier type="VolumeIssueCount">3</identifier><part><date>1991</date><detail type="volume"><number>50</number><caption>vol.</caption></detail><detail type="issue"><number>1-3</number><caption>no.</caption></detail><extent unit="pages"><start>259</start><end>274</end></extent></part><recordInfo><recordOrigin>The Mathematical Programming Society, Inc., 1991</recordOrigin></recordInfo></relatedItem><identifier type="istex">3B37B634372137461C168E3123E1753159BD3187</identifier><identifier type="DOI">10.1007/BF01594938</identifier><identifier type="ArticleID">BF01594938</identifier><identifier type="ArticleID">Art17</identifier><accessCondition type="use and reproduction" contentType="copyright">The Mathematical Programming Society, Inc., 1991</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>The Mathematical Programming Society, Inc., 1991</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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