On solving a D.C. programming problem by a sequence of linear programs
Identifieur interne : 001014 ( Istex/Corpus ); précédent : 001013; suivant : 001015On solving a D.C. programming problem by a sequence of linear programs
Auteurs : R. Horst ; T. Q. Phong ; Ng. V. Thoai ; J. De VriesSource :
- Journal of Global Optimization [ 0925-5001 ] ; 1991-06-01.
Abstract
Abstract: We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ℝ n . This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.
Url:
DOI: 10.1007/BF00119991
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ISTEX:71F67D56BA26BC0C09663960B7F6B61E3AA1B752Le document en format XML
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Horst</name><affiliation><mods:affiliation>Fachbereich IV-Mathematik, Universität Trier, Trier, West Germany</mods:affiliation></affiliation></author><author><name sortKey="Phong, T Q" sort="Phong, T Q" uniqKey="Phong T" first="T. Q." last="Phong">T. Q. Phong</name><affiliation><mods:affiliation>Institute of Technology, Danang, Vietnam</mods:affiliation></affiliation></author><author><name sortKey="Thoai, Ng V" sort="Thoai, Ng V" uniqKey="Thoai N" first="Ng. V." last="Thoai">Ng. V. Thoai</name><affiliation><mods:affiliation>Institute of Mathematics, Hanoi, Vietnam</mods:affiliation></affiliation></author><author><name sortKey="De Vries, J" sort="De Vries, J" uniqKey="De Vries J" first="J." last="De Vries">J. 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This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.</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><json:item><name>T. Q. Phong</name><affiliations><json:string>Institute of Technology, Danang, Vietnam</json:string></affiliations></json:item><json:item><name>Ng. V. Thoai</name><affiliations><json:string>Institute of Mathematics, Hanoi, Vietnam</json:string></affiliations></json:item><json:item><name>J. de Vries</name><affiliations><json:string>Fachbereich IV-Mathematik, Universität Trier, Trier, West Germany</json:string></affiliations></json:item></author><articleId><json:string>BF00119991</json:string><json:string>Art6</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ℝ n . This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.</abstract><qualityIndicators><score>5.708</score><pdfVersion>1.3</pdfVersion><pdfPageSize>453.24 x 677.12 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>349</abstractCharCount><pdfWordCount>6431</pdfWordCount><pdfCharCount>36498</pdfCharCount><pdfPageCount>21</pdfPageCount><abstractWordCount>59</abstractWordCount></qualityIndicators><title>On solving a D.C. programming problem by a sequence of linear programs</title><refBibs><json:item><host><author><json:item><name>H,P Benson</name></json:item></author><title>Separable Concave Minimization via Partial Outer Approximation and Branch and Bound, forthcoming in Operations Research Letters</title><publicationDate>1991</publicationDate></host></json:item><json:item><host><author><json:item><name>H,P Benson</name></json:item><json:item><name>R Horst</name></json:item></author><title>A Branch and Bound-Outer Approximation Algorithm for Concave Minimization over a Convex Set</title><publicationDate>1991</publicationDate></host></json:item><json:item><author><json:item><name>J,E Falk</name></json:item><json:item><name>K,R Hoffman</name></json:item></author><host><volume>1</volume><pages><last>280</last><first>271</first></pages><author></author><title>Mathematics of Operations Research</title><publicationDate>1976</publicationDate></host><title>A Successive Underestimation Method for Concave Minimization Problems</title><publicationDate>1976</publicationDate></json:item><json:item><author><json:item><name>F Giannessi</name></json:item><json:item><name>L Jurina</name></json:item><json:item><name>G Maier</name></json:item></author><host><volume>1</volume><pages><last>91</last><first>81</first></pages><author></author><title>Engineering Structures</title><publicationDate>1979</publicationDate></host><title>Optimal Excavation Profile for a Pipeline Freely Resting on the Sea Floor</title><publicationDate>1979</publicationDate></json:item><json:item><author><json:item><name>B Heron</name></json:item><json:item><name>M Sermange</name></json:item></author><host><pages><last>382</last><first>351</first></pages><author></author><title>Nonconvex Methods for Computing Free Boundary Equilibria of Axially Symmetric Plasmas</title><publicationDate>1982</publicationDate></host><title>Generalize Differentiability, Duality and Optimization for Problems Dealing with Differences of Convex Functions</title><publicationDate>1982</publicationDate></json:item><json:item><author><json:item><name>K,L Hoffman</name></json:item></author><host><volume>20</volume><pages><last>32</last><first>22</first></pages><author></author><title>Mathematical Programming</title><publicationDate>1981</publicationDate></host><title>A Method for Globally Minmizing Concave Functions over Convex Sets</title><publicationDate>1981</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>10</volume><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>R Horst</name></json:item></author><host><volume>19</volume><pages><last>238</last><first>237</first></pages><author></author><title>Mathematical Programming</title><publicationDate>1980</publicationDate></host><title>A Note on the Convergence of an Algorithm for Nonconvex Programming Problems</title><publicationDate>1980</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><pages><last>291</last><first>271</first></pages><author></author><title>A General Class of Branch and Bound Methods in Global Optimization with Some New Approaches for Concave Minimization</title><publicationDate>1986</publicationDate></host><publicationDate>1986</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>58</volume><pages><last>37</last><first>11</first></pages><author></author><title>J. of Optimization Theory and Application</title><publicationDate>1988</publicationDate></host><title>Deterministic Global Optimization with Partition Sets Whose Feasibility is Not Known. Application to Concave Minimization, Reverse Convex Constraints, D.C.-Programming an'd Lipschitzian Optimization</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>61</volume><pages><last>146</last><first>143</first></pages><author></author><title>J. of Optimization Theory and Applictions</title><publicationDate>1989</publicationDate></host><title>On Consistency of Bounding Operations in Deterministic Global Optimization</title><publicationDate>1989</publicationDate></json:item><json:item><author><json:item><name>R Horst</name></json:item></author><host><volume>37</volume><pages><last>471</last><first>433</first></pages><author></author><title>Naval Research Logistics</title><publicationDate>1990</publicationDate></host><title>Deterministic Global Optimization: Recent Advances and New Fields of Application</title><publicationDate>1990</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 Thoai</name></json:item></author><host><volume>25</volume><pages><first>18</first></pages><issue>1</issue><author></author><title>Annals of Operations Research</title><publicationDate>1990</publicationDate></host><title>On Solving General Reverse 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></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><json:item><name>H,P Benson</name></json:item></author><host><author></author><title>Concave Minimization via Conical Partitions and Polyhedral Outer Approximation, forthcoming in Mathematical Programming</title><publicationDate>1991</publicationDate></host><publicationDate>1991</publicationDate></json:item><json:item><author><json:item><name>R Ho&</name></json:item><json:item><name>N,V Thoai</name></json:item><json:item><name>H Tuy</name></json:item></author><host><volume>9</volume><pages><last>159</last><first>153</first></pages><issue>3</issue><author></author><title>Operations Research Spektrum</title><publicationDate>1987</publicationDate></host><title>Outer Approximation by Polyhedral Convex Sets</title><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>H Tuy</name></json:item></author><host><volume>20</volume><pages><last>264</last><first>255</first></pages><author></author><title>Optimization</title><publicationDate>1989</publicationDate></host><title>On an Outer Approximation Concept in Global Optimization</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><json:item><name>De Vries</name></json:item><json:item><name>J </name></json:item></author><host><volume>7</volume><pages><last>90</last><first>85</first></pages><author></author><title>Operations Research Letters</title><publicationDate>1987</publicationDate></host><title>On Finding New Vertices and Redundant Constraints in Cutting Plane Algorithms for Global Optimization</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>R Hors&</name></json:item><json:item><name>H Tuy</name></json:item></author><host><volume>54</volume><pages><last>271</last><first>253</first></pages><author></author><title>J. of Optimization Theory and Applications</title><publicationDate>1987</publicationDate></host><title>On the Convergence of Global Methods in Multiextremal Optimization</title><publicationDate>1987</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>1990</publicationDate></host><publicationDate>1990</publicationDate></json:item><json:item><host><author><json:item><name>V,H Nguyen</name></json:item><json:item><name>J,J Strodiot</name></json:item></author><title>Computing a Global Solution to a Design Centering Problem</title><publicationDate>1988</publicationDate></host></json:item><json:item><author><json:item><name>P,M Pardalos</name></json:item><json:item><name>J,H Glick</name></json:item><json:item><name>J,B Rosen</name></json:item></author><host><pages><last>291</last><first>281</first></pages><author></author><title>Global Minimization of Indefinite Quadratic Problems</title><publicationDate>1987</publicationDate></host><publicationDate>1987</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><author></author><title>Constrained Global Optimization: Algorithms and Applications</title><publicationDate>1987</publicationDate></host><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>E Polak</name></json:item></author><host><volume>29</volume><pages><last>89</last><first>21</first></pages><author></author><title>On the Mathematical Foundations of Nondifferentiable Optimization in Engineering Design, SIAM Review</title><publicationDate>1987</publicationDate></host><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>E Polak</name></json:item><json:item><name>A,S Vincentelly</name></json:item></author><host><pages><last>813</last><first>795</first></pages><author></author><title>Theoretical and Computational Aspects of the Optimal Design Centering Tolerancing and Tuning Problem, IEEE Transactions Circuits and Systems CAS-26</title><publicationDate>1979</publicationDate></host><publicationDate>1979</publicationDate></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>P,T Thach</name></json:item></author><host><volume>41</volume><pages><last>248</last><first>229</first></pages><author></author><title>C. Program, Mathematical Programming</title><publicationDate>1988</publicationDate></host><title>The Design Centering Problem as a D</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>T,V Thieu</name></json:item><json:item><name>B,T Tam</name></json:item><json:item><name>V,T Ban</name></json:item></author><host><volume>8</volume><pages><last>40</last><first>21</first></pages><author></author><title>Acta Mathematics Vietnamica</title><publicationDate>1983</publicationDate></host><title>An Outer Approximation Method for Globally Minimizing a Concave Function over a Compact Convex Set</title><publicationDate>1983</publicationDate></json:item><json:item><author><json:item><name>N,V Thoai</name></json:item></author><host><volume>19</volume><pages><last>674</last><first>665</first></pages><author></author><title>Optimization</title><publicationDate>1988</publicationDate></host><title>A Modified Version of Tuy's Method for Solving D.C. Programming Problems</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>J,F Toland</name></json:item></author><host><volume>71</volume><pages><last>61</last><first>41</first></pages><author></author><title>Archive of Radional Mechanics and Analysis</title><publicationDate>1979</publicationDate></host><title>A Duality Principle for Nonconvex Optimization and the Calculus of Variations</title><publicationDate>1979</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item></author><host><volume>8</volume><pages><last>34</last><first>3</first></pages><author></author><title>Acta Mathematics Vietnamica</title><publicationDate>1983</publicationDate></host><title>On Outer Approximation Methods for Solving Concave Minimization Problems</title><publicationDate>1983</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>A General Deterministic Approach to Global Optimization via D.C. Programming Fermat Days</title><publicationDate>1985</publicationDate></host><publicationDate>1985</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item></author><host><volume>52</volume><pages><last>485</last><first>463</first></pages><author></author><title>J. of Optimization Theory and Applications</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><pages><last>182</last><first>150</first></pages><author></author><title>Effect of the Subdivision Strategy on Convergence and Efficiency of Some Global Optimization Algorithms</title><publicationDate>1987</publicationDate></host><title>Global Minimization of a Difference of Two Convex Functions</title><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item><json:item><name>R Horst</name></json:item></author><host><volume>41</volume><pages><last>183</last><first>161</first></pages><author></author><title>Mathematical Programming</title><publicationDate>1988</publicationDate></host><title>Convergence and Restart in Branch and Bound Algorithms for Global SOLVING A D.C. PROGRAMMING PROBLEM 203 Optimization. Application to Concave Minimization and DC-Optimization Problems</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item><json:item><name>T,V Thieu</name></json:item><json:item><name>N,Q Thai</name></json:item></author><host><volume>10</volume><pages><last>514</last><first>498</first></pages><author></author><title>Mathematics of Operations Research</title><publicationDate>1985</publicationDate></host><title>A Conical Algorithm for Globally Minimizing a Concave Function over a Closed Convex Set</title><publicationDate>1985</publicationDate></json:item><json:item><author><json:item><name>H Tuy</name></json:item><json:item><name>N,V Thuong</name></json:item></author><host><volume>18</volume><pages><last>142</last><first>119</first></pages><author></author><title>Applied Mathematics and Optimization</title><publicationDate>1988</publicationDate></host><title>On the Global Minimization of a Convex Function under General Nonconvex Constraints</title><publicationDate>1988</publicationDate></json:item><json:item><author><json:item><name>L,M Vidigal</name></json:item><json:item><name>S,W Director</name></json:item></author><host><pages><last>24</last><first>13</first></pages><author></author><title>IEEE Transactions on Computer-Aided-Design of Zntegrated Circuits and Systems CAD-I</title><publicationDate>1982</publicationDate></host><title>A Design Centering Algorithm for Nonconvex Regions of Acceptability</title><publicationDate>1982</publicationDate></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>1</volume><pages><last>203</last><first>183</first></pages><issn><json:string>0925-5001</json:string></issn><issue>2</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 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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, 1991</p></availability><date>1990-05-28</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">On solving a D.C. programming problem by a sequence of linear programs</title><author xml:id="author-1"><persName><forename type="first">R.</forename><surname>Horst</surname></persName><affiliation>Fachbereich IV-Mathematik, Universität Trier, Trier, West Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">T.</forename><surname>Phong</surname></persName><affiliation>Institute of Technology, Danang, Vietnam</affiliation></author><author xml:id="author-3"><persName><forename type="first">Ng.</forename><surname>Thoai</surname></persName><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation></author><author xml:id="author-4"><persName><forename type="first">J.</forename><surname>de Vries</surname></persName><affiliation>Fachbereich IV-Mathematik, Universität Trier, Trier, West Germany</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">7</idno><idno type="volume-issue-count">4</idno><imprint><publisher>Kluwer Academic 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This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.</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="1990-05-28">Created</change><change when="1991-06-01">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-22">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>1</VolumeIDStart><VolumeIDEnd>1</VolumeIDEnd><VolumeIssueCount>4</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo 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programs</ArticleTitle><ArticleFirstPage>183</ArticleFirstPage><ArticleLastPage>203</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2004</Year><Month>5</Month><Day>18</Day></RegistrationDate><Received><Year>1990</Year><Month>5</Month><Day>28</Day></Received><Accepted><Year>1990</Year><Month>12</Month><Day>4</Day></Accepted></ArticleHistory><ArticleCopyright><CopyrightHolderName>Kluwer Academic Publishers</CopyrightHolderName><CopyrightYear>1991</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 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IV-Mathematik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><City>Trier</City><Country>West Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Institute of Technology</OrgName><OrgAddress><City>Danang</City><Country>Vietnam</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>Institute of Mathematics</OrgName><OrgAddress><City>Hanoi</City><Country>Vietnam</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>. This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.</Para></Abstract><KeywordGroup Language="En"><Heading>Key words</Heading><Keyword>Nonlinear programming</Keyword><Keyword>global optimization</Keyword><Keyword>d.c. programming</Keyword><Keyword>branch and bound</Keyword><Keyword>outer approximation</Keyword><Keyword>prismatic partition</Keyword></KeywordGroup><ArticleNote Type="Misc"><SimplePara>Parts of this research were accomplished while the third author was visiting the University of Trier, Germany, as a fellow of the Alexander von Humboldt foundation.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>On solving a D.C. programming problem by a sequence of linear programs</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>On solving a D.C. programming problem by a sequence of linear programs</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></name><name type="personal"><namePart type="given">T.</namePart><namePart type="given">Q.</namePart><namePart type="family">Phong</namePart><affiliation>Institute of Technology, Danang, Vietnam</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Ng.</namePart><namePart type="given">V.</namePart><namePart type="family">Thoai</namePart><affiliation>Institute of Mathematics, Hanoi, Vietnam</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J.</namePart><namePart type="family">de Vries</namePart><affiliation>Fachbereich IV-Mathematik, Universität Trier, Trier, West 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">1990-05-28</dateCreated><dateIssued encoding="w3cdtf">1991-06-01</dateIssued><copyrightDate encoding="w3cdtf">1991</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: We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ℝ n . This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.</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">1991-06-01</dateIssued><copyrightDate encoding="w3cdtf">1991</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">7</identifier><identifier type="VolumeIssueCount">4</identifier><part><date>1991</date><detail type="volume"><number>1</number><caption>vol.</caption></detail><detail type="issue"><number>2</number><caption>no.</caption></detail><extent unit="pages"><start>183</start><end>203</end></extent></part><recordInfo><recordOrigin>Kluwer Academic Publishers, 1991</recordOrigin></recordInfo></relatedItem><identifier type="istex">71F67D56BA26BC0C09663960B7F6B61E3AA1B752</identifier><identifier type="DOI">10.1007/BF00119991</identifier><identifier type="ArticleID">BF00119991</identifier><identifier type="ArticleID">Art6</identifier><accessCondition type="use and reproduction" contentType="copyright">Kluwer Academic Publishers, 1991</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Kluwer Academic Publishers, 1991</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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