On the convergence of global methods in multiextremal optimization
Identifieur interne : 001200 ( Istex/Corpus ); précédent : 001199; suivant : 001201On the convergence of global methods in multiextremal optimization
Auteurs : R. Horst ; H. TuySource :
- Journal of Optimization Theory and Applications [ 0022-3239 ] ; 1987-08-01.
Abstract
Abstract: A general class of derivative-free optimization procedures is presented including the corresponding convergence theory. This theory turns out to be very constructive, in the sense that the convergence conditions not only can be verified easily for many existing algorithms, but also allow one to construct new procedures. It is shown that popular methods such as branch-and-bound concepts, Pintér's general class of procedures, the algorithms of Pijavskii, Shubert, and Mladineo, and the approach of Zheng and Galperin can not only be subsumed under this class of methods, but also partly be improved by regarding them within the framework presented.
Url:
DOI: 10.1007/BF00939434
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ISTEX:B759147BD55CE37A8617326DE667278AADA749A8Le document en format XML
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Tuy</name><affiliation><mods:affiliation>Institute of Mathematics, Bo Hô, Hanoi, Vietnam</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Journal of Optimization Theory and Applications</title><title level="j" type="abbrev">J Optim Theory Appl</title><idno type="ISSN">0022-3239</idno><idno type="eISSN">1573-2878</idno><imprint><publisher>Kluwer Academic Publishers-Plenum Publishers</publisher><pubPlace>New York</pubPlace><date type="published" when="1987-08-01">1987-08-01</date><biblScope unit="volume">54</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="253">253</biblScope><biblScope unit="page" to="271">271</biblScope></imprint><idno type="ISSN">0022-3239</idno></series><idno type="istex">B759147BD55CE37A8617326DE667278AADA749A8</idno><idno type="DOI">10.1007/BF00939434</idno><idno type="ArticleID">BF00939434</idno><idno type="ArticleID">Art3</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0022-3239</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: A general class of derivative-free optimization procedures is presented including the corresponding convergence theory. This theory turns out to be very constructive, in the sense that the convergence conditions not only can be verified easily for many existing algorithms, but also allow one to construct new procedures. It is shown that popular methods such as branch-and-bound concepts, Pintér's general class of procedures, the algorithms of Pijavskii, Shubert, and Mladineo, and the approach of Zheng and Galperin can not only be subsumed under this class of methods, but also partly be improved by regarding them within the framework presented.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>R. Horst</name><affiliations><json:string>Fachbereich IV-Mathematik, Universität Trier, Trier, Germany</json:string></affiliations></json:item><json:item><name>H. 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It is shown that popular methods such as branch-and-bound concepts, Pintér's general class of procedures, the algorithms of Pijavskii, Shubert, and Mladineo, and the approach of Zheng and Galperin can not only be subsumed under this class of methods, but also partly be improved by regarding them within the framework presented.</abstract><qualityIndicators><score>6.188</score><pdfVersion>1.3</pdfVersion><pdfPageSize>432 x 648 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>660</abstractCharCount><pdfWordCount>5420</pdfWordCount><pdfCharCount>26169</pdfCharCount><pdfPageCount>19</pdfPageCount><abstractWordCount>99</abstractWordCount></qualityIndicators><title>On the convergence of global methods in multiextremal optimization</title><refBibs><json:item><author><json:item><name>Horst </name></json:item><json:item><name>R </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>Class of Branch-and-Bound Methods in Global Optimization with Some New Approaches for Concave Minimization</title><publicationDate>1986</publicationDate></json:item><json:item><host><author><json:item><name>Horst </name></json:item><json:item><name>R </name></json:item><json:item><name>Tuy </name></json:item><json:item><name>H </name></json:item></author><title>Remarks on Convergence and Finiteness of Branch-and- Bound Algorithms in Global Optimization</title><publicationDate>1985</publicationDate></host></json:item><json:item><author><json:item><name>Pinter </name></json:item><json:item><name>J </name></json:item></author><host><author></author><title>Istituto per le Applicazioni della Matematica e dell</title><publicationDate>1983</publicationDate></host><title>A Unified Approach to Globally Convergent One-Dimensional Optimization Algorithms</title><publicationDate>1983</publicationDate></json:item><json:item><host><pages><last>16</last><first>1</first></pages><author><json:item><name>Pinter </name></json:item><json:item><name>J </name></json:item></author><title>Globally Convergent Methods for N-Dimensional Multiextremal Optimization, Optimization</title><publicationDate>1986</publicationDate></host></json:item><json:item><author><json:item><name>Q Zrteng</name></json:item><json:item><name>B Jiang</name></json:item><json:item><name>Zhuang </name></json:item><json:item><name>S </name></json:item></author><host><volume>2</volume><pages><last>174</last><first>164</first></pages><author></author><title>Acta Mathematicae Applagatea Sinica</title><publicationDate>1978</publicationDate></host><title>A Method for Finding the GlobaI Extremum</title><publicationDate>1978</publicationDate></json:item><json:item><author><json:item><name>Galperin </name></json:item><json:item><name>E </name></json:item><json:item><name>A </name></json:item><json:item><name>Zheng </name></json:item><json:item><name>Q </name></json:item></author><host><pages><last>628</last><first>620</first></pages><author></author><title>Proceedings of the 1983 Conference on Information Sciences and Systems</title><publicationDate>1983</publicationDate></host><title>Nonlinear Observation via Global Optimization Methods</title><publicationDate>1983</publicationDate></json:item><json:item><author><json:item><name>Galperin </name></json:item><json:item><name>E,A </name></json:item></author><host><volume>112</volume><pages><last>640</last><first>635</first></pages><author></author><title>Journal of Mathematical Analysis and Applications</title><publicationDate>1985</publicationDate></host><title>The Cubic Algorithm</title><publicationDate>1985</publicationDate></json:item><json:item><author><json:item><name>Pijavskii </name></json:item><json:item><name>S,A </name></json:item></author><host><volume>2</volume><pages><last>67</last><first>57</first></pages><author></author><title>USSR Computational Mathematics and Mathematical Physics</title><publicationDate>1972</publicationDate></host><title>An Algorithm for Finding the Absolute Extremum of a Function</title><publicationDate>1972</publicationDate></json:item><json:item><author><json:item><name>Shubert </name></json:item><json:item><name>B,O </name></json:item></author><host><volume>9</volume><pages><last>388</last><first>379</first></pages><author></author><title>SIAM Journal of Numerical Analysis</title><publicationDate>1972</publicationDate></host><title>A Sequential Method Seeking the Global Maximum of a Function</title><publicationDate>1972</publicationDate></json:item><json:item><author><json:item><name>Mladineo </name></json:item><json:item><name>R,H </name></json:item></author><host><author></author><title>presented at the 12th International Symposium on Mathematical Programming</title><publicationDate>1985</publicationDate></host><title>An Algorithm for Finding the Global Maximum of a Multi. modal, Multivariate function</title><publicationDate>1985</publicationDate></json:item><json:item><author><json:item><name>Horst </name></json:item><json:item><name>R </name></json:item></author><host><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>Thoai </name></json:item><json:item><name>N,V </name></json:item><json:item><name>Tuy </name></json:item><json:item><name>H </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><host><author><json:item><name>Strongin </name></json:item><json:item><name>R,G </name></json:item></author><title>Numerical &lethods for Multiextremal Problems</title><publicationDate>1978</publicationDate></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>54</volume><pages><last>271</last><first>253</first></pages><issn><json:string>0022-3239</json:string></issn><issue>2</issue><subject><json:item><value>Theory of Computation</value></json:item><json:item><value>Applications of Mathematics</value></json:item><json:item><value>Optimization</value></json:item><json:item><value>Calculus of 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This theory turns out to be very constructive, in the sense that the convergence conditions not only can be verified easily for many existing algorithms, but also allow one to construct new procedures. It is shown that popular methods such as branch-and-bound concepts, Pintér's general class of procedures, the algorithms of Pijavskii, Shubert, and Mladineo, and the approach of Zheng and Galperin can not only be subsumed under this class of methods, but also partly be improved by regarding them within the framework presented.</p></abstract><textClass><keywords scheme="Journal Subject"><list><head>Mathematics</head><item><term>Theory of Computation</term></item><item><term>Applications of Mathematics</term></item><item><term>Optimization</term></item><item><term>Calculus of Variations and Optimal Control</term></item><item><term>Optimization</term></item><item><term>Engineering, general</term></item><item><term>Operation Research/Decision Theory</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1987-08-01">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-22">References added</change><change xml:id="refBibs-istex" 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DisplayOrder="Western"><GivenName>R.</GivenName><FamilyName>Horst</FamilyName></AuthorName><Role>Professor</Role></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>H.</GivenName><FamilyName>Tuy</FamilyName></AuthorName><Role>Professor</Role></Author><Affiliation ID="Aff1"><OrgDivision>Fachbereich IV-Mathematik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><City>Trier</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Institute of Mathematics, Bo Hô</OrgName><OrgAddress><City>Hanoi</City><Country>Vietnam</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>A general class of derivative-free optimization procedures is presented including the corresponding convergence theory. This theory turns out to be very constructive, in the sense that the convergence conditions not only can be verified easily for many existing algorithms, but also allow one to construct new procedures. It is shown that popular methods such as branch-and-bound concepts, Pintér's general class of procedures, the algorithms of Pijavskii, Shubert, and Mladineo, and the approach of Zheng and Galperin can not only be subsumed under this class of methods, but also partly be improved by regarding them within the framework presented.</Para></Abstract><KeywordGroup Language="En"><Heading>Key Words</Heading><Keyword>Global optimization</Keyword><Keyword>multiextremal optimization</Keyword><Keyword>optimization algorithms</Keyword><Keyword>nonlinear programming</Keyword><Keyword>branch-and-bound methods</Keyword><Keyword>Lipschitzian optimization</Keyword></KeywordGroup><ArticleNote Type="CommunicatedBy"><SimplePara>Communicated by G. 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This theory turns out to be very constructive, in the sense that the convergence conditions not only can be verified easily for many existing algorithms, but also allow one to construct new procedures. It is shown that popular methods such as branch-and-bound concepts, Pintér's general class of procedures, the algorithms of Pijavskii, Shubert, and Mladineo, and the approach of Zheng and Galperin can not only be subsumed under this class of methods, but also partly be improved by regarding them within the framework presented.</abstract><note>Contributed Papers</note><relatedItem type="host"><titleInfo><title>Journal of Optimization Theory and Applications</title></titleInfo><titleInfo type="abbreviated"><title>J Optim Theory Appl</title></titleInfo><genre type="journal" displayLabel="Archive Journal"></genre><originInfo><dateIssued encoding="w3cdtf">1987-08-01</dateIssued><copyrightDate encoding="w3cdtf">1987</copyrightDate></originInfo><subject><genre>Mathematics</genre><topic>Theory of Computation</topic><topic>Applications of Mathematics</topic><topic>Optimization</topic><topic>Calculus of Variations and Optimal Control</topic><topic>Optimization</topic><topic>Engineering, general</topic><topic>Operation Research/Decision Theory</topic></subject><identifier type="ISSN">0022-3239</identifier><identifier type="eISSN">1573-2878</identifier><identifier type="JournalID">10957</identifier><identifier type="IssueArticleCount">15</identifier><identifier type="VolumeIssueCount">3</identifier><part><date>1987</date><detail type="volume"><number>54</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="pages"><start>253</start><end>271</end></extent></part><recordInfo><recordOrigin>Plenum Publishing Corporation, 1987</recordOrigin></recordInfo></relatedItem><identifier type="istex">B759147BD55CE37A8617326DE667278AADA749A8</identifier><identifier type="DOI">10.1007/BF00939434</identifier><identifier type="ArticleID">BF00939434</identifier><identifier type="ArticleID">Art3</identifier><accessCondition type="use and reproduction" contentType="copyright">Plenum Publishing Corporation, 1987</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Plenum Publishing Corporation, 1987</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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