Maximizing a concave function over the efficient or weakly-efficient set
Identifieur interne : 001212 ( Istex/Corpus ); précédent : 001211; suivant : 001213Maximizing a concave function over the efficient or weakly-efficient set
Auteurs : Reiner Horst ; Nguyen V. ThoaiSource :
- European Journal of Operational Research [ 0377-2217 ] ; 1999.
Abstract
An important approach in multiple criteria linear programming is the optimization of some function over the efficient or weakly-efficient set. This is a very difficult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the efficient or weakly-efficient set. We show that this problem can essentially be formulated as a special global optimization problem in the space of the extreme criteria of the underlying multiple criteria linear program. An algorithm of branch and bound type is proposed for solving the resulting problem.
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DOI: 10.1016/S0377-2217(98)00230-6
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Box 3825, 54286 Trier, Germany</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:469F45F613CE075DC5BF169092462A1B1928F31B</idno><date when="1999" year="1999">1999</date><idno type="doi">10.1016/S0377-2217(98)00230-6</idno><idno type="url">https://api.istex.fr/document/469F45F613CE075DC5BF169092462A1B1928F31B/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001212</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001212</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">Maximizing a concave function over the efficient or weakly-efficient set</title><author><name sortKey="Horst, Reiner" sort="Horst, Reiner" uniqKey="Horst R" first="Reiner" last="Horst">Reiner Horst</name><affiliation><mods:affiliation>Department of Mathematics, University of Trier, P.O. Box 3825, 54286 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>Department of Mathematics, University of Trier, P.O. Box 3825, 54286 Trier, Germany</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">European Journal of Operational Research</title><title level="j" type="abbrev">EOR</title><idno type="ISSN">0377-2217</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1999">1999</date><biblScope unit="volume">117</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="239">239</biblScope><biblScope unit="page" to="252">252</biblScope></imprint><idno type="ISSN">0377-2217</idno></series><idno type="istex">469F45F613CE075DC5BF169092462A1B1928F31B</idno><idno type="DOI">10.1016/S0377-2217(98)00230-6</idno><idno type="PII">S0377-2217(98)00230-6</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0377-2217</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">An important approach in multiple criteria linear programming is the optimization of some function over the efficient or weakly-efficient set. This is a very difficult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the efficient or weakly-efficient set. We show that this problem can essentially be formulated as a special global optimization problem in the space of the extreme criteria of the underlying multiple criteria linear program. An algorithm of branch and bound type is proposed for solving the resulting problem.</div></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>Reiner Horst</name><affiliations><json:string>Department of Mathematics, University of Trier, P.O. Box 3825, 54286 Trier, Germany</json:string></affiliations></json:item><json:item><name>Nguyen V. Thoai</name><affiliations><json:string>Department of Mathematics, University of Trier, P.O. 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This is a very difficult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the efficient or weakly-efficient set. We show that this problem can essentially be formulated as a special global optimization problem in the space of the extreme criteria of the underlying multiple criteria linear program. An algorithm of branch and bound type is proposed for solving the resulting problem.</abstract><qualityIndicators><score>6.212</score><pdfVersion>1.2</pdfVersion><pdfPageSize>544 x 743 pts</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>5</keywordCount><abstractCharCount>650</abstractCharCount><pdfWordCount>6988</pdfWordCount><pdfCharCount>29444</pdfCharCount><pdfPageCount>14</pdfPageCount><abstractWordCount>101</abstractWordCount></qualityIndicators><title>Maximizing a concave function over the efficient or weakly-efficient set</title><pii><json:string>S0377-2217(98)00230-6</json:string></pii><refBibs><json:item><author><json:item><name>H.P. Benson</name></json:item></author><host><volume>98</volume><pages><last>580</last><first>562</first></pages><author></author><title>Journal of Mathematical Analysis and Applications</title></host><title>Optimization over the efficient set</title></json:item><json:item><author><json:item><name>H.B. Benson</name></json:item></author><host><volume>1</volume><pages><last>104</last><first>83</first></pages><author></author><title>Journal of Global Optimization</title></host><title>An all-linear programming relaxation algorithm for optimizing over the efficient set</title></json:item><json:item><author><json:item><name>H.P. Benson</name></json:item></author><host><volume>73</volume><pages><last>64</last><first>47</first></pages><author></author><title>Journal of Optimization Theory and Applications</title></host><title>A finite, nonadjacent extreme-point search algorithm for optimizing over the efficient set</title></json:item><json:item><author><json:item><name>H.P. Benson</name></json:item></author><host><volume>6</volume><pages><last>251</last><first>231</first></pages><author></author><title>Journal of Global Optimization</title></host><title>A geometrical analysis of the outcome set in multiple objective convex programs with linear criterion functions</title></json:item><json:item><author><json:item><name>H.P. Benson</name></json:item><json:item><name>D. Lee</name></json:item></author><host><volume>88</volume><pages><last>105</last><first>77</first></pages><author></author><title>Journal of Optimization Theory and Applications</title></host><title>Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem</title></json:item><json:item><author><json:item><name>S. 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Thoai</name></json:item></author><host><volume>74</volume><pages><last>486</last><first>469</first></pages><author></author><title>Journal of Optimization Theory and Applications</title></host><title>Conical algorithm for the global minimization of linear constrained decomposable concave minimization problems</title></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>92</volume><pages><last>635</last><first>609</first></pages><author></author><title>Journal of Optimization Theory and Applications</title></host><title>Utility function programs and optimization over the efficient set in multiple-objective decision making</title></json:item><json:item><host><author></author></host></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></host><title>Concave minimization via conical partitions and polyhedral outer approximation</title></json:item><json:item><author><json:item><name>L.M. Muu</name></json:item></author><host><volume>23</volume><pages><last>105</last><first>83</first></pages><author></author><title>Vietnam Journal of Mathematics</title></host><title>Computational aspect of optimization problems over the efficient set</title></json:item><json:item><author><json:item><name>J. Philip</name></json:item></author><host><volume>2</volume><pages><last>229</last><first>207</first></pages><author></author><title>Mathematical Programming</title></host><title>Algorithms for the vector maximization problem</title></json:item><json:item><host><author></author></host></json:item><json:item><host><author></author></host></json:item><json:item><host><author></author></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>117</volume><pii><json:string>S0377-2217(00)X0107-5</json:string></pii><pages><last>252</last><first>239</first></pages><issn><json:string>0377-2217</json:string></issn><issue>2</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>European Journal of Operational Research</title><publicationDate>1999</publicationDate></host><categories><wos><json:string>science</json:string><json:string>operations research & management science</json:string></wos><scienceMetrix><json:string>applied sciences</json:string><json:string>engineering</json:string><json:string>operations research</json:string></scienceMetrix></categories><publicationDate>1999</publicationDate><copyrightDate>1999</copyrightDate><doi><json:string>10.1016/S0377-2217(98)00230-6</json:string></doi><id>469F45F613CE075DC5BF169092462A1B1928F31B</id><score>1.7478188</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/469F45F613CE075DC5BF169092462A1B1928F31B/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/469F45F613CE075DC5BF169092462A1B1928F31B/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/469F45F613CE075DC5BF169092462A1B1928F31B/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Maximizing a concave function over the efficient or weakly-efficient set</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>ELSEVIER</publisher><availability><p>©1999 Elsevier Science B.V.</p></availability><date>1999</date></publicationStmt><notesStmt><note>Research supported by the “Deutsche Forschungsgemeinschaft” through the “Graduiertenkolleg Mathematische Optimierung” at the University of Trier and through the project DECOMP.</note><note type="content">Section title: Theory and Methodology</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Maximizing a concave function over the efficient or weakly-efficient set</title><author xml:id="author-1"><persName><forename type="first">Reiner</forename><surname>Horst</surname></persName><note type="correspondence"><p>Corresponding author. Tel.: +49 651 2013475; fax: +49 651 2013479; e-mail: horst@uni-trier.de</p></note><affiliation>Department of Mathematics, University of Trier, P.O. Box 3825, 54286 Trier, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">Nguyen V.</forename><surname>Thoai</surname></persName><affiliation>Department of Mathematics, University of Trier, P.O. Box 3825, 54286 Trier, Germany</affiliation></author></analytic><monogr><title level="j">European Journal of Operational Research</title><title level="j" type="abbrev">EOR</title><idno type="pISSN">0377-2217</idno><idno type="PII">S0377-2217(00)X0107-5</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1999"></date><biblScope unit="volume">117</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="239">239</biblScope><biblScope unit="page" to="252">252</biblScope></imprint></monogr><idno type="istex">469F45F613CE075DC5BF169092462A1B1928F31B</idno><idno type="DOI">10.1016/S0377-2217(98)00230-6</idno><idno type="PII">S0377-2217(98)00230-6</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1999</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>An important approach in multiple criteria linear programming is the optimization of some function over the efficient or weakly-efficient set. 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An algorithm of branch and bound type is proposed for solving the resulting problem.</p></abstract><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>Multiple criteria analysis</term></item><item><term>Optimization over efficient/weakly-efficient sets</term></item><item><term>Nonconvex programming</term></item><item><term>Global optimization</term></item><item><term>Branch and bound</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1999">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/469F45F613CE075DC5BF169092462A1B1928F31B/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: body; tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>EOR</jid><aid>3631</aid><ce:pii>S0377-2217(98)00230-6</ce:pii><ce:doi>10.1016/S0377-2217(98)00230-6</ce:doi><ce:copyright year="1999" type="full-transfer">Elsevier Science B.V.</ce:copyright></item-info><head><ce:dochead><ce:textfn>Theory and Methodology</ce:textfn></ce:dochead><ce:title>Maximizing a concave function over the efficient or weakly-efficient set<ce:footnote id="FN1"><ce:label>1</ce:label><ce:note-para>Research supported by the “Deutsche Forschungsgemeinschaft” through the “Graduiertenkolleg Mathematische Optimierung” at the University of Trier and through the project DECOMP.</ce:note-para></ce:footnote><ce:cross-ref refid="FN1"><ce:sup>1</ce:sup></ce:cross-ref></ce:title><ce:author-group><ce:author><ce:given-name>Reiner</ce:given-name><ce:surname>Horst</ce:surname><ce:cross-ref refid="CORR1">*</ce:cross-ref></ce:author><ce:author><ce:given-name>Nguyen V.</ce:given-name><ce:surname>Thoai</ce:surname></ce:author><ce:affiliation><ce:textfn>Department of Mathematics, University of Trier, P.O. Box 3825, 54286 Trier, Germany</ce:textfn></ce:affiliation><ce:correspondence id="CORR1"><ce:label>*</ce:label><ce:text>Corresponding author. Tel.: +49 651 2013475; fax: +49 651 2013479; e-mail: horst@uni-trier.de</ce:text></ce:correspondence></ce:author-group><ce:date-received day="2" month="4" year="1997"></ce:date-received><ce:date-accepted day="3" month="6" year="1998"></ce:date-accepted><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>An important approach in multiple criteria linear programming is the optimization of some function over the efficient or weakly-efficient set. This is a very difficult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the efficient or weakly-efficient set. We show that this problem can essentially be formulated as a special global optimization problem in the space of the extreme criteria of the underlying multiple criteria linear program. An algorithm of branch and bound type is proposed for solving the resulting problem.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="keyword"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>Multiple criteria analysis</ce:text></ce:keyword><ce:keyword><ce:text>Optimization over efficient/weakly-efficient sets</ce:text></ce:keyword><ce:keyword><ce:text>Nonconvex programming</ce:text></ce:keyword><ce:keyword><ce:text>Global optimization</ce:text></ce:keyword><ce:keyword><ce:text>Branch and bound</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Maximizing a concave function over the efficient or weakly-efficient set</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Maximizing a concave function over the efficient or weakly-efficient set</title></titleInfo><name type="personal"><namePart type="given">Reiner</namePart><namePart type="family">Horst</namePart><affiliation>Department of Mathematics, University of Trier, P.O. Box 3825, 54286 Trier, Germany</affiliation><description>Corresponding author. Tel.: +49 651 2013475; fax: +49 651 2013479; e-mail: horst@uni-trier.de</description><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Nguyen V.</namePart><namePart type="family">Thoai</namePart><affiliation>Department of Mathematics, University of Trier, P.O. Box 3825, 54286 Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1999</dateIssued><copyrightDate encoding="w3cdtf">1999</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">An important approach in multiple criteria linear programming is the optimization of some function over the efficient or weakly-efficient set. This is a very difficult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the efficient or weakly-efficient set. We show that this problem can essentially be formulated as a special global optimization problem in the space of the extreme criteria of the underlying multiple criteria linear program. An algorithm of branch and bound type is proposed for solving the resulting problem.</abstract><note type="footnote">Research supported by the “Deutsche Forschungsgemeinschaft” through the “Graduiertenkolleg Mathematische Optimierung” at the University of Trier and through the project DECOMP.</note><note type="content">Section title: Theory and Methodology</note><subject><genre>Keywords</genre><topic>Multiple criteria analysis</topic><topic>Optimization over efficient/weakly-efficient sets</topic><topic>Nonconvex programming</topic><topic>Global optimization</topic><topic>Branch and bound</topic></subject><relatedItem type="host"><titleInfo><title>European Journal of Operational Research</title></titleInfo><titleInfo type="abbreviated"><title>EOR</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">19990901</dateIssued></originInfo><identifier type="ISSN">0377-2217</identifier><identifier type="PII">S0377-2217(00)X0107-5</identifier><part><date>19990901</date><detail type="volume"><number>117</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="issue pages"><start>199</start><end>414</end></extent><extent unit="pages"><start>239</start><end>252</end></extent></part></relatedItem><identifier type="istex">469F45F613CE075DC5BF169092462A1B1928F31B</identifier><identifier type="DOI">10.1016/S0377-2217(98)00230-6</identifier><identifier type="PII">S0377-2217(98)00230-6</identifier><accessCondition type="use and reproduction" contentType="copyright">©1999 Elsevier Science B.V.</accessCondition><recordInfo><recordContentSource>ELSEVIER</recordContentSource><recordOrigin>Elsevier Science B.V., ©1999</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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