Constraint decomposition algorithms in global optimization
Identifieur interne : 001293 ( Istex/Corpus ); précédent : 001292; suivant : 001294Constraint decomposition algorithms in global optimization
Auteurs : Reiner Horst ; Nguyen Van ThoaiSource :
- Journal of Global Optimization [ 0925-5001 ] ; 1994-12-01.
Abstract
Abstract: Many global optimization problems can be formulated in the form min{c(x, y): x εX, y εY, (x, y) εZ, y εG} where X, Y are polytopes in ℝ p , ℝ n , respectively, Z is a closed convex set in ℝp+n, while G is the complement of an open convex set in ℝ n . The function c:ℝ p+n → ℝ is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in ℝ n . Computational experiments show that the resulting algorithms work well for problems with smalln.
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DOI: 10.1007/BF01096683
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The function c:ℝ p+n → ℝ is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in ℝ n . Computational experiments show that the resulting algorithms work well for problems with smalln.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Reiner Horst</name><affiliations><json:string>Fachbereich IV-Mathematik, Universitaet Trier, D-54286, Trier, Germany</json:string></affiliations></json:item><json:item><name>Nguyen van Thoai</name><affiliations><json:string>Fachbereich IV-Mathematik, Universitaet Trier, D-54286, Trier, Germany</json:string></affiliations></json:item></author><articleId><json:string>BF01096683</json:string><json:string>Art3</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Many global optimization problems can be formulated in the form min{c(x, y): x εX, y εY, (x, y) εZ, y εG} where X, Y are polytopes in ℝ p , ℝ n , respectively, Z is a closed convex set in ℝp+n, while G is the complement of an open convex set in ℝ n . The function c:ℝ p+n → ℝ is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in ℝ n . Computational experiments show that the resulting algorithms work well for problems with smalln.</abstract><qualityIndicators><score>6.404</score><pdfVersion>1.3</pdfVersion><pdfPageSize>453.568 x 684 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>652</abstractCharCount><pdfWordCount>6209</pdfWordCount><pdfCharCount>27875</pdfCharCount><pdfPageCount>16</pdfPageCount><abstractWordCount>117</abstractWordCount></qualityIndicators><title>Constraint decomposition algorithms in global optimization</title><refBibs><json:item><author><json:item><name>E,C Chen</name></json:item><json:item><name>E Hansen</name></json:item><json:item><name>Jaumard,B </name></json:item></author><host><volume>10</volume><pages><last>409</last><first>403</first></pages><author></author><title>Operations Research Letters</title><publicationDate>1991</publicationDate></host><title>On-Line and Off-Line Vertex Enumeration by Adjacency Lists</title><publicationDate>1991</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></author><host><volume>74</volume><pages><last>486</last><first>469</first></pages><author></author><title>J. Opt. Theory a. Appl</title><publicationDate>1992</publicationDate></host><title>Conical Algorithm for the Global Minimisation of Linearly Constrained Decomposable Concave Minimization Problems</title><publicationDate>1992</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item><json:item><name>H Tuy</name></json:item></author><host><author></author><title>Global Optimization: Deterministic Approaches</title><publicationDate>1993</publicationDate></host><publicationDate>1993</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item><json:item><name>T,Q Phong</name></json:item><json:item><name>N,V Thaoi</name></json:item></author><host><volume>25</volume><pages><last>18</last><first>1</first></pages><author></author><title>Annals ofOper. Res</title><publicationDate>1990</publicationDate></host><title>On Solving General Reserve Convex Programming Problems by a Sequence of Linear Programs and Line Searches</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><json:item><name>H,P Benson</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><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><pages><last>159</last><first>153</first></pages><author></author><title>Outer Approximation by Polyhedral Convex Sets</title><publicationDate>1987</publicationDate></host><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>2</volume><pages><last>19</last><first>1</first></pages><author></author><title>Journal Global Optimization</title><publicationDate>1992</publicationDate></host><title>A New Simplical Cover Technique in Constrained Global Optimization</title><publicationDate>1992</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>25</volume><pages><last>64</last><first>53</first></pages><author></author><title>Optimization</title><publicationDate>1992</publicationDate></host><title>On Geometry and Convergence of a Class of Simplicial Covers</title><publicationDate>1992</publicationDate></json:item><json:item><author><json:item><name>L,D Muu</name></json:item></author><host><volume>61</volume><pages><last>87</last><first>75</first></pages><author></author><title>Mathematical Programming</title><publicationDate>1993</publicationDate></host><title>An Algorithm for Solving Convex Programs with an Additional Convex-Concave Constraint</title><publicationDate>1993</publicationDate></json:item><json:item><author><json:item><name>P,T Thach</name></json:item><json:item><name>R,E Burkard</name></json:item><json:item><name>W Oettli</name></json:item></author><host><pages><last>154</last><first>145</first></pages><author></author><title>Mathematical Programs with a Two-dimensional Reverse Convex Constraint</title><publicationDate>1991</publicationDate></host><publicationDate>1991</publicationDate></json:item><json:item><author><json:item><name>N,V Thoai</name></json:item></author><host><volume>1</volume><pages><last>357</last><first>341</first></pages><author></author><title>J. Global Optimization</title><publicationDate>1991</publicationDate></host><title>A Global Optimization Approach for Solving the Convex Multiplicative Programming Problem</title><publicationDate>1991</publicationDate></json:item><json:item><author><json:item><name>N,V Thoai</name></json:item></author><host><volume>50</volume><pages><last>253</last><first>241</first></pages><author></author><title>Computing</title><publicationDate>1993</publicationDate></host><title>Canonical D.C. Programming Techniques for Solving a Convex Program with an Additional Constraint of Multiplication Type</title><publicationDate>1993</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><pages><last>352</last><first>335</first></pages><author></author><title>Concave Minimization under Linear Constraints with Special Structure</title><publicationDate>1985</publicationDate></host><publicationDate>1985</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item></author><host><pages><last>162</last><first>137</first></pages><author></author><title>Fermat Days</title><publicationDate>1985</publicationDate></host><title>A General Deterministic Approach to Global Optimization via D.C. Programming</title><publicationDate>1985</publicationDate></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>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></author><host><volume>2</volume><pages><last>40</last><first>21</first></pages><author></author><title>J. 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The function c:ℝ p+n → ℝ is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in ℝ n . Computational experiments show that the resulting algorithms work well for problems with smalln.</p></abstract><textClass><keywords scheme="Journal Subject"><list><head>Economics / Management Science</head><item><term>Computer Science, general</term></item><item><term>Real Functions</term></item><item><term>Optimization</term></item><item><term>Operation Research/Decision Theory</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1993-07-09">Created</change><change when="1994-12-01">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-23">References added</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-21">References 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Global Optimization</JournalTitle><JournalSubTitle>An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management, and Engineer</JournalSubTitle><JournalAbbreviatedTitle>J Glob Optim</JournalAbbreviatedTitle><JournalSubjectGroup><JournalSubject Type="Primary">Economics / Management Science</JournalSubject><JournalSubject Type="Secondary">Computer Science, general</JournalSubject><JournalSubject Type="Secondary">Real Functions</JournalSubject><JournalSubject Type="Secondary">Optimization</JournalSubject><JournalSubject Type="Secondary">Operation Research/Decision Theory</JournalSubject></JournalSubjectGroup></JournalInfo><Volume><VolumeInfo VolumeType="Regular" TocLevels="0"><VolumeIDStart>5</VolumeIDStart><VolumeIDEnd>5</VolumeIDEnd><VolumeIssueCount>4</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo TocLevels="0"><IssueIDStart>4</IssueIDStart><IssueIDEnd>4</IssueIDEnd><IssueArticleCount>11</IssueArticleCount><IssueHistory><CoverDate><Year>1994</Year><Month>12</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>Kluwer Academic Publishers</CopyrightHolderName><CopyrightYear>1994</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art3"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF01096683</ArticleID><ArticleDOI>10.1007/BF01096683</ArticleDOI><ArticleSequenceNumber>3</ArticleSequenceNumber><ArticleTitle Language="En">Constraint decomposition algorithms in global optimization</ArticleTitle><ArticleFirstPage>333</ArticleFirstPage><ArticleLastPage>348</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>1</Month><Day>19</Day></RegistrationDate><Received><Year>1993</Year><Month>7</Month><Day>9</Day></Received><Accepted><Year>1994</Year><Month>2</Month><Day>24</Day></Accepted></ArticleHistory><ArticleCopyright><CopyrightHolderName>Kluwer Academic Publishers</CopyrightHolderName><CopyrightYear>1994</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>10898</JournalID><VolumeIDStart>5</VolumeIDStart><VolumeIDEnd>5</VolumeIDEnd><IssueIDStart>4</IssueIDStart><IssueIDEnd>4</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Reiner</GivenName><FamilyName>Horst</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Nguyen</GivenName><Particle>van</Particle><FamilyName>Thoai</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgDivision>Fachbereich IV-Mathematik</OrgDivision><OrgName>Universitaet Trier</OrgName><OrgAddress><Postcode>D-54286</Postcode><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Many global optimization problems can be formulated in the form min{<Emphasis Type="Italic">c(x, y): x</Emphasis> ε<Emphasis Type="Italic">X, y</Emphasis> ε<Emphasis Type="Italic">Y, (x, y)</Emphasis> ε<Emphasis Type="Italic">Z, y</Emphasis> ε<Emphasis Type="Italic">G}</Emphasis> where X, Y are polytopes in ℝ<Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>, ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>, respectively, Z is a closed convex set in ℝ<Superscript>p+n</Superscript>, while G is the complement of an open convex set in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>. The function c:ℝ<Superscript><Emphasis Type="Italic">p+n</Emphasis></Superscript> → ℝ is assumed to be linear. Using the fact that the nonconvex constraints depend only upon the<Emphasis Type="Italic">y</Emphasis>-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>. Computational experiments show that the resulting algorithms work well for problems with small<Emphasis Type="Italic">n</Emphasis>.</Para></Abstract><KeywordGroup Language="En"><Heading>Key words</Heading><Keyword>Global optimization</Keyword><Keyword>decomposition</Keyword><Keyword>canonical d.c. program</Keyword><Keyword>conical branch and bound algorithms</Keyword><Keyword>outer approximation</Keyword><Keyword>cutting plane algorithms</Keyword></KeywordGroup></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Constraint decomposition algorithms in global optimization</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Constraint decomposition algorithms in global optimization</title></titleInfo><name type="personal"><namePart type="given">Reiner</namePart><namePart type="family">Horst</namePart><affiliation>Fachbereich IV-Mathematik, Universitaet Trier, D-54286, Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Nguyen</namePart><namePart type="family">van Thoai</namePart><affiliation>Fachbereich IV-Mathematik, Universitaet Trier, D-54286, Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper"></genre><originInfo><publisher>Kluwer Academic Publishers</publisher><place><placeTerm type="text">Dordrecht</placeTerm></place><dateCreated encoding="w3cdtf">1993-07-09</dateCreated><dateIssued encoding="w3cdtf">1994-12-01</dateIssued><copyrightDate encoding="w3cdtf">1994</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 global optimization problems can be formulated in the form min{c(x, y): x εX, y εY, (x, y) εZ, y εG} where X, Y are polytopes in ℝ p , ℝ n , respectively, Z is a closed convex set in ℝp+n, while G is the complement of an open convex set in ℝ n . The function c:ℝ p+n → ℝ is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in ℝ n . Computational experiments show that the resulting algorithms work well for problems with smalln.</abstract><relatedItem type="host"><titleInfo><title>Journal of Global Optimization</title><subTitle>An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management, and Engineer</subTitle></titleInfo><titleInfo type="abbreviated"><title>J Glob Optim</title></titleInfo><genre type="journal" displayLabel="Archive Journal"></genre><originInfo><dateIssued encoding="w3cdtf">1994-12-01</dateIssued><copyrightDate encoding="w3cdtf">1994</copyrightDate></originInfo><subject><genre>Economics / Management Science</genre><topic>Computer Science, general</topic><topic>Real Functions</topic><topic>Optimization</topic><topic>Operation Research/Decision Theory</topic></subject><identifier type="ISSN">0925-5001</identifier><identifier type="eISSN">1573-2916</identifier><identifier type="JournalID">10898</identifier><identifier type="IssueArticleCount">11</identifier><identifier type="VolumeIssueCount">4</identifier><part><date>1994</date><detail type="volume"><number>5</number><caption>vol.</caption></detail><detail type="issue"><number>4</number><caption>no.</caption></detail><extent unit="pages"><start>333</start><end>348</end></extent></part><recordInfo><recordOrigin>Kluwer Academic Publishers, 1994</recordOrigin></recordInfo></relatedItem><identifier type="istex">43E9EAADA9A098581FAC850D150A7BF24269EB66</identifier><identifier type="DOI">10.1007/BF01096683</identifier><identifier type="ArticleID">BF01096683</identifier><identifier type="ArticleID">Art3</identifier><accessCondition type="use and reproduction" contentType="copyright">Kluwer Academic Publishers, 1994</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Kluwer Academic Publishers, 1994</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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