On consistency of bounding operations in deterministic global optimization
Identifieur interne : 000419 ( Istex/Corpus ); précédent : 000418; suivant : 000420On consistency of bounding operations in deterministic global optimization
Auteurs : R. HorstSource :
- Journal of Optimization Theory and Applications [ 0022-3239 ] ; 1989-04-01.
Abstract
Abstract: This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of Ref. 1. A necessary clarification is given of the notion of convergence φq → φ in Lemma 2.1, and a derivation of Proposition 2.1 is presented that includes a new and simple consistency proof of the classical bounding by convex envelopes used in many branch-and-bound procedures.
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DOI: 10.1007/BF00940850
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Horst</name><affiliation><mods:affiliation>Fachbereich IV—Mathematik, Universität Trier, Trier, West Germany</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:7DE63C345653140B60C9D76135F61E9F965A66FC</idno><date when="1989" year="1989">1989</date><idno type="doi">10.1007/BF00940850</idno><idno type="url">https://api.istex.fr/document/7DE63C345653140B60C9D76135F61E9F965A66FC/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000419</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000419</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">On consistency of bounding operations in deterministic global optimization</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, Trier, West Germany</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="1989-04-01">1989-04-01</date><biblScope unit="volume">61</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="143">143</biblScope><biblScope unit="page" to="146">146</biblScope></imprint><idno type="ISSN">0022-3239</idno></series><idno type="istex">7DE63C345653140B60C9D76135F61E9F965A66FC</idno><idno type="DOI">10.1007/BF00940850</idno><idno type="ArticleID">BF00940850</idno><idno type="ArticleID">Art11</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: This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of Ref. 1. A necessary clarification is given of the notion of convergence φq → φ in Lemma 2.1, and a derivation of Proposition 2.1 is presented that includes a new and simple consistency proof of the classical bounding by convex envelopes used in many branch-and-bound procedures.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>R. Horst</name><affiliations><json:string>Fachbereich IV—Mathematik, Universität Trier, Trier, West Germany</json:string></affiliations></json:item></author><articleId><json:string>BF00940850</json:string><json:string>Art11</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of Ref. 1. 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</name></json:item></author><host><volume>8</volume><pages><last>286</last><first>273</first></pages><author></author><title>Mathematics of Operations Research</title></host><title>Jointly Constrained Biconvex Programming</title></json:item><json:item><host><author><json:item><name>J Dteudonne</name></json:item></author><title>Foundations of Modern Analysis</title><publicationDate>1968</publicationDate></host></json:item><json:item><author><json:item><name>Kall </name></json:item><json:item><name>P </name></json:item></author><host><volume>11</volume><pages><last>17</last><first>8</first></pages><author></author><title>Mathematics of Operations Research</title><publicationDate>1986</publicationDate></host><title>Approximation to Optimization Problems: An Elementary 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DisplayOrder="Western"><GivenName>R.</GivenName><FamilyName>Horst</FamilyName></AuthorName><Role>Professor</Role></Author><Affiliation ID="Aff1"><OrgDivision>Fachbereich IV—Mathematik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><City>Trier</City><Country>West Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of Ref. 1. A necessary clarification is given of the notion of convergence φ<Subscript>q</Subscript> → φ in Lemma 2.1, and a derivation of Proposition 2.1 is presented that includes a new and simple consistency proof of the classical bounding by convex envelopes used in many branch-and-bound procedures.</Para></Abstract><KeywordGroup Language="En"><Heading>Key Words</Heading><Keyword>Global optimization</Keyword><Keyword>nonconvex programming</Keyword><Keyword>mathematical programming</Keyword><Keyword>branch-and-bound methods</Keyword></KeywordGroup><ArticleNote Type="CommunicatedBy"><SimplePara>Communicated by G. Leitmann</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On consistency of bounding operations in deterministic global optimization</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>On consistency of bounding operations in deterministic global optimization</title></titleInfo><name type="personal"><namePart type="given">R.</namePart><namePart type="family">Horst</namePart><affiliation>Fachbereich IV—Mathematik, Universität Trier, Trier, West Germany</affiliation><role><roleTerm type="text">author</roleTerm></role><description>Professor</description></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper"></genre><originInfo><publisher>Kluwer Academic Publishers-Plenum Publishers</publisher><place><placeTerm type="text">New York</placeTerm></place><dateIssued encoding="w3cdtf">1989-04-01</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: This technical comment refers to the discussion of strong consistency of several bounding procedures in Lemma 2.1 and Proposition 2.1 of Ref. 1. A necessary clarification is given of the notion of convergence φq → φ in Lemma 2.1, and a derivation of Proposition 2.1 is presented that includes a new and simple consistency proof of the classical bounding by convex envelopes used in many branch-and-bound procedures.</abstract><note>Technical Comment</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">1989-04-01</dateIssued><copyrightDate encoding="w3cdtf">1989</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">16</identifier><identifier type="VolumeIssueCount">3</identifier><part><date>1989</date><detail type="volume"><number>61</number><caption>vol.</caption></detail><detail type="issue"><number>1</number><caption>no.</caption></detail><extent unit="pages"><start>143</start><end>146</end></extent></part><recordInfo><recordOrigin>Plenum Publishing Corporation, 1989</recordOrigin></recordInfo></relatedItem><identifier type="istex">7DE63C345653140B60C9D76135F61E9F965A66FC</identifier><identifier type="DOI">10.1007/BF00940850</identifier><identifier type="ArticleID">BF00940850</identifier><identifier type="ArticleID">Art11</identifier><accessCondition type="use and reproduction" contentType="copyright">Plenum Publishing Corporation, 1989</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Plenum Publishing Corporation, 1989</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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