A generalized duality and applications
Identifieur interne : 001202 ( Istex/Corpus ); précédent : 001201; suivant : 001203A generalized duality and applications
Auteurs : Phan Thien ThachSource :
- Journal of Global Optimization [ 0925-5001 ] ; 1993-09-01.
Abstract
Abstract: The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.
Url:
DOI: 10.1007/BF01096773
Links to Exploration step
ISTEX:6369B0ABB5D587C36C03C2FA81D391C417ACD617Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">A generalized duality and applications</title><author><name sortKey="Thach, Phan Thien" sort="Thach, Phan Thien" uniqKey="Thach P" first="Phan Thien" last="Thach">Phan Thien Thach</name><affiliation><mods:affiliation>Institute of Human and Social Sciences, Tokyo Institute of Technology, Japan</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:6369B0ABB5D587C36C03C2FA81D391C417ACD617</idno><date when="1993" year="1993">1993</date><idno type="doi">10.1007/BF01096773</idno><idno type="url">https://api.istex.fr/document/6369B0ABB5D587C36C03C2FA81D391C417ACD617/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001202</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001202</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">A generalized duality and applications</title><author><name sortKey="Thach, Phan Thien" sort="Thach, Phan Thien" uniqKey="Thach P" first="Phan Thien" last="Thach">Phan Thien Thach</name><affiliation><mods:affiliation>Institute of Human and Social Sciences, Tokyo Institute of Technology, Japan</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Journal of Global Optimization</title><title level="j" type="sub">An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management, and Engineer</title><title level="j" type="abbrev">J Glob Optim</title><idno type="ISSN">0925-5001</idno><idno type="eISSN">1573-2916</idno><imprint><publisher>Kluwer Academic Publishers</publisher><pubPlace>Dordrecht</pubPlace><date type="published" when="1993-09-01">1993-09-01</date><biblScope unit="volume">3</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="311">311</biblScope><biblScope unit="page" to="324">324</biblScope></imprint><idno type="ISSN">0925-5001</idno></series><idno type="istex">6369B0ABB5D587C36C03C2FA81D391C417ACD617</idno><idno type="DOI">10.1007/BF01096773</idno><idno type="ArticleID">BF01096773</idno><idno type="ArticleID">Art3</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0925-5001</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>Phan Thien Thach</name><affiliations><json:string>Institute of Human and Social Sciences, Tokyo Institute of Technology, Japan</json:string></affiliations></json:item></author><articleId><json:string>BF01096773</json:string><json:string>Art3</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.</abstract><qualityIndicators><score>6.193</score><pdfVersion>1.3</pdfVersion><pdfPageSize>453.28 x 684 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>631</abstractCharCount><pdfWordCount>4909</pdfWordCount><pdfCharCount>21719</pdfCharCount><pdfPageCount>14</pdfPageCount><abstractWordCount>107</abstractWordCount></qualityIndicators><title>A generalized duality and applications</title><refBibs><json:item><author><json:item><name>J,P Aubin</name></json:item><json:item><name>1 Ekeland</name></json:item></author><host><pages><last>245</last><first>225</first></pages><author></author><title>Estimates of the duality gap in nonconvex optimization</title><publicationDate>1976</publicationDate></host><publicationDate>1976</publicationDate></json:item><json:item><author><json:item><name>R,E Burkard</name></json:item><json:item><name>H,W Hamacher</name></json:item><json:item><name>J Tind</name></json:item></author><host><volume>26</volume><pages><last>209</last><first>197</first></pages><author></author><title>Zeitschrift fur Oper. Res</title><publicationDate>1982</publicationDate></host><title>On abstract duality in mathematical programming</title><publicationDate>1982</publicationDate></json:item><json:item><author><json:item><name>J,E Falk</name></json:item><json:item><name>K,L Hoffman</name></json:item></author><host><volume>1</volume><pages><last>259</last><first>251</first></pages><author></author><title>Math. Oper. Res</title><publicationDate>1976</publicationDate></host><title>A successive underestimating method for concave minimization problems</title><publicationDate>1976</publicationDate></json:item><json:item><author><json:item><name>R,J Hillestad</name></json:item><json:item><name>S,E Jacobsen</name></json:item></author><host><pages><last>78</last><first>63</first></pages><author></author><title>Reverse convex programming</title><publicationDate>1980</publicationDate></host><publicationDate>1980</publicationDate></json:item><json:item><author><json:item><name>J,B Hiriart-Urruty</name></json:item></author><host><volume>256</volume><pages><last>70</last><first>37</first></pages><author></author><title>Lecture Notes in Economics and Mathematical Systems</title><publicationDate>1984</publicationDate></host><title>Generalized differentiability, duality and optimization for problems dealing with differences of convex functions</title><publicationDate>1984</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>5</volume><pages><last>210</last><first>205</first></pages><author></author><title>European J. Oper. Res</title><publicationDate>1980</publicationDate></host><title>A note on the dual gap in nonconvex optimization and a very simple procedure for bild evaluation type problems</title><publicationDate>1980</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</title><publicationDate>1990</publicationDate></host><publicationDate>1990</publicationDate></json:item><json:item><author><json:item><name>H Konno</name></json:item><json:item><name>T Kuno</name></json:item></author><host><pages><last>64</last><first>51</first></pages><author></author><title>Linear multiplicative programming</title><publicationDate>1992</publicationDate></host><publicationDate>1992</publicationDate></json:item><json:item><host><pages><last>273</last><first>259</first></pages><author><json:item><name>H Konno</name></json:item><json:item><name>Y Yajima</name></json:item></author><title>Minimizing and maximizing the product of linear fractional functions, Recent Advances in Global Optimization</title><publicationDate>1982</publicationDate></host></json:item><json:item><author><json:item><name>L,D Muu</name></json:item></author><host><volume>21</volume><pages><last>435</last><first>428</first></pages><author></author><title>Kybernetika (Praha)</title><publicationDate>1985</publicationDate></host><title>A convergent algorithm for solving linear programs with an additional reverse convex constraint</title><publicationDate>1985</publicationDate></json:item><json:item><author><json:item><name>W Oettli</name></json:item></author><host><pages><last>238</last><first>227</first></pages><author></author><title>Generalized Concavity in Optimization and Economics</title><publicationDate>1981</publicationDate></host><title>Optimality condition involving generalized convex mappings</title><publicationDate>1981</publicationDate></json:item><json:item><author><json:item><name>W Oettli</name></json:item></author><host><pages><last>226</last><first>196</first></pages><author></author><title>Modern Applied Mathematics</title><publicationDate>1982</publicationDate></host><title>Optimality condition for programming problems involving multivalued mapping</title><publicationDate>1982</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><pages><first>268</first></pages><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><host><author><json:item><name>B,N Pshenichnyyi</name></json:item></author><title>Lecons sur jeux differentials, controle optimal et jeux differentiels, Cahiers de IIRIA</title><publicationDate>1971</publicationDate></host></json:item><json:item><author><json:item><name>R,T Rockafellar</name></json:item></author><host><author></author><title>Convex Analysis</title><publicationDate>1970</publicationDate></host><publicationDate>1970</publicationDate></json:item><json:item><author><json:item><name>J,B Rosen</name></json:item><json:item><name>P,M Pardalos</name></json:item></author><host><volume>34</volume><pages><last>174</last><first>163</first></pages><author></author><title>Math. Prog</title><publicationDate>1986</publicationDate></host><title>Global minimization of large-scale constrained concave quadratic problems by separable programming</title><publicationDate>1986</publicationDate></json:item><json:item><host><pages><last>234</last><first>221</first></pages><author><json:item><name>I Singer</name></json:item></author><title>Minimization of continuous convex functionals on complements of convex sets of locally convex spaces, Optimization U</title><publicationDate>1980</publicationDate></host></json:item><json:item><author><json:item><name>P,T Thach</name></json:item></author><host><volume>159</volume><pages><last>322</last><first>299</first></pages><author></author><title>J. Math. Anal. Appl</title><publicationDate>1991</publicationDate></host><title>Quasiconjugates of functions, duality relationship between quasiconvex minimization under a reverse convex constraint and quasiconvex maximization under a convex constraint, and applications</title><publicationDate>1991</publicationDate></json:item><json:item><author><json:item><name>P,T Thach</name></json:item><json:item><name>R Burkard</name></json:item><json:item><name>W Oettli</name></json:item></author><host><volume>1</volume><pages><last>154</last><first>145</first></pages><author></author><title>J. Global Optimization</title><publicationDate>1991</publicationDate></host><title>Mathematical programs with a two-dimensional reverse convex constraint</title><publicationDate>1991</publicationDate></json:item><json:item><host><author><json:item><name>P,T Thach</name></json:item><json:item><name>H Tuy</name></json:item></author><title>Dual Outer Approximation Methods for Concave Programs and Reverse Convex Programs, IHSS 90-30, Institute of Human and Social Sciences</title><publicationDate>1990</publicationDate></host></json:item><json:item><host><author><json:item><name>P,T Thach</name></json:item></author><title>Global optimality criterions and a duality with a zero gap in nonconvex optimization problems</title><publicationDate>1991</publicationDate></host></json:item><json:item><host><author><json:item><name>P,T Thach</name></json:item><json:item><name>H Konno</name></json:item></author><title>A Generalized Dantzig-Wolfe Decomposition Principle for a Class of Nonconvex Programming Problems, IHSS 92-47, Institute of Human and Social Sciences</title><publicationDate>1992</publicationDate></host></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>Math. 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>J Tind</name></json:item><json:item><name>L,A Wolsey</name></json:item></author><host><volume>21</volume><pages><last>261</last><first>241</first></pages><author></author><title>Math. Prog</title><publicationDate>1981</publicationDate></host><title>An elementary survey of general duality theory in mathematical programming</title><publicationDate>1981</publicationDate></json:item><json:item><author><json:item><name>J,F Toland</name></json:item></author><host><volume>66</volume><pages><last>415</last><first>399</first></pages><author></author><title>J. Math. Anal. Appl</title><publicationDate>1978</publicationDate></host><title>Duality in nonconvex optimization</title><publicationDate>1978</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item></author><host><volume>159</volume><pages><last>35</last><first>32</first></pages><author></author><title>Doklady Akademia Nauka SSSR</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></author><host><volume>52</volume><pages><last>486</last><first>463</first></pages><author></author><title>J. Optim. Theory and Appl</title><publicationDate>1987</publicationDate></host><title>Convex programs with an additional reverse convex constraint</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item></author><host><volume>129</volume><pages><last>303</last><first>273</first></pages><author></author><title>Mathematics Studies</title><publicationDate>1987</publicationDate></host><title>A general deterministic approach to global optimization via d.c. programming</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item></author><host><volume>1</volume><pages><last>244</last><first>229</first></pages><author></author><title>J. Global Optimization</title><publicationDate>1991</publicationDate></host><title>Polyhedral annexation, dualization and dimension reduction technique in global optimization</title><publicationDate>1991</publicationDate></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>3</volume><pages><last>324</last><first>311</first></pages><issn><json:string>0925-5001</json:string></issn><issue>3</issue><subject><json:item><value>Computer Science, general</value></json:item><json:item><value>Real Functions</value></json:item><json:item><value>Optimization</value></json:item><json:item><value>Operation Research/Decision Theory</value></json:item></subject><journalId><json:string>10898</json:string></journalId><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1573-2916</json:string></eissn><title>Journal of Global Optimization</title><publicationDate>1993</publicationDate><copyrightDate>1993</copyrightDate></host><categories><wos><json:string>science</json:string><json:string>operations research & management science</json:string><json:string>mathematics, applied</json:string></wos><scienceMetrix><json:string>applied sciences</json:string><json:string>engineering</json:string><json:string>operations research</json:string></scienceMetrix></categories><publicationDate>1993</publicationDate><copyrightDate>1993</copyrightDate><doi><json:string>10.1007/BF01096773</json:string></doi><id>6369B0ABB5D587C36C03C2FA81D391C417ACD617</id><score>0.017944252</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/6369B0ABB5D587C36C03C2FA81D391C417ACD617/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/6369B0ABB5D587C36C03C2FA81D391C417ACD617/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/6369B0ABB5D587C36C03C2FA81D391C417ACD617/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">A generalized duality and applications</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>Kluwer Academic Publishers</publisher><pubPlace>Dordrecht</pubPlace><availability><p>Kluwer Academic Publishers, 1993</p></availability><date>1990-12-17</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">A generalized duality and applications</title><author xml:id="author-1"><persName><forename type="first">Phan</forename><surname>Thach</surname></persName><affiliation>Institute of Human and Social Sciences, Tokyo Institute of Technology, Japan</affiliation></author></analytic><monogr><title level="j">Journal of Global Optimization</title><title level="j" type="sub">An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management, and Engineer</title><title level="j" type="abbrev">J Glob Optim</title><idno type="journal-ID">10898</idno><idno type="pISSN">0925-5001</idno><idno type="eISSN">1573-2916</idno><idno type="issue-article-count">8</idno><idno type="volume-issue-count">4</idno><imprint><publisher>Kluwer Academic Publishers</publisher><pubPlace>Dordrecht</pubPlace><date type="published" when="1993-09-01"></date><biblScope unit="volume">3</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="311">311</biblScope><biblScope unit="page" to="324">324</biblScope></imprint></monogr><idno type="istex">6369B0ABB5D587C36C03C2FA81D391C417ACD617</idno><idno type="DOI">10.1007/BF01096773</idno><idno type="ArticleID">BF01096773</idno><idno type="ArticleID">Art3</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1990-12-17</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.</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="1990-12-17">Created</change><change when="1993-09-01">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 added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/6369B0ABB5D587C36C03C2FA81D391C417ACD617/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Springer, Publisher found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType><istex:document><Publisher><PublisherInfo><PublisherName>Kluwer Academic Publishers</PublisherName><PublisherLocation>Dordrecht</PublisherLocation></PublisherInfo><Journal><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>10898</JournalID><JournalPrintISSN>0925-5001</JournalPrintISSN><JournalElectronicISSN>1573-2916</JournalElectronicISSN><JournalTitle>Journal of 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>3</VolumeIDStart><VolumeIDEnd>3</VolumeIDEnd><VolumeIssueCount>4</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo TocLevels="0"><IssueIDStart>3</IssueIDStart><IssueIDEnd>3</IssueIDEnd><IssueArticleCount>8</IssueArticleCount><IssueHistory><CoverDate><DateString>Autumn 1993</DateString><Year>1993</Year><Month>9</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>Kluwer Academic Publishers</CopyrightHolderName><CopyrightYear>1993</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art3"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF01096773</ArticleID><ArticleDOI>10.1007/BF01096773</ArticleDOI><ArticleSequenceNumber>3</ArticleSequenceNumber><ArticleTitle Language="En">A generalized duality and applications</ArticleTitle><ArticleFirstPage>311</ArticleFirstPage><ArticleLastPage>324</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>1</Month><Day>19</Day></RegistrationDate><Received><Year>1990</Year><Month>12</Month><Day>17</Day></Received><Accepted><Year>1992</Year><Month>10</Month><Day>20</Day></Accepted></ArticleHistory><ArticleCopyright><CopyrightHolderName>Kluwer Academic Publishers</CopyrightHolderName><CopyrightYear>1993</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>3</VolumeIDStart><VolumeIDEnd>3</VolumeIDEnd><IssueIDStart>3</IssueIDStart><IssueIDEnd>3</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Phan</GivenName><GivenName>Thien</GivenName><FamilyName>Thach</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgDivision>Institute of Human and Social Sciences</OrgDivision><OrgName>Tokyo Institute of Technology</OrgName><OrgAddress><Country>Japan</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.</Para></Abstract><KeywordGroup Language="En"><Heading>Key words</Heading><Keyword>Nonconvex duality</Keyword><Keyword>zero gap</Keyword><Keyword>global optimization</Keyword></KeywordGroup><ArticleNote Type="Misc"><SimplePara>On leave from the Institute of Mathematics, Hanoi, Vietnam.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A generalized duality and applications</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>A generalized duality and applications</title></titleInfo><name type="personal"><namePart type="given">Phan</namePart><namePart type="given">Thien</namePart><namePart type="family">Thach</namePart><affiliation>Institute of Human and Social Sciences, Tokyo Institute of Technology, Japan</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">1990-12-17</dateCreated><dateIssued encoding="w3cdtf">1993-09-01</dateIssued><copyrightDate encoding="w3cdtf">1993</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: The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.</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">1993-09-01</dateIssued><copyrightDate encoding="w3cdtf">1993</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">8</identifier><identifier type="VolumeIssueCount">4</identifier><part><date>1993</date><detail type="volume"><number>3</number><caption>vol.</caption></detail><detail type="issue"><number>3</number><caption>no.</caption></detail><extent unit="pages"><start>311</start><end>324</end></extent></part><recordInfo><recordOrigin>Kluwer Academic Publishers, 1993</recordOrigin></recordInfo></relatedItem><identifier type="istex">6369B0ABB5D587C36C03C2FA81D391C417ACD617</identifier><identifier type="DOI">10.1007/BF01096773</identifier><identifier type="ArticleID">BF01096773</identifier><identifier type="ArticleID">Art3</identifier><accessCondition type="use and reproduction" contentType="copyright">Kluwer Academic Publishers, 1993</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Kluwer Academic Publishers, 1993</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001202 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 001202 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Rhénanie
|area= UnivTrevesV1
|flux= Istex
|étape= Corpus
|type= RBID
|clé= ISTEX:6369B0ABB5D587C36C03C2FA81D391C417ACD617
|texte= A generalized duality and applications
}}
| This area was generated with Dilib version V0.6.31. |  |