Conical algorithm for the global minimization of linearly constrained decomposable concave minimization problems
Identifieur interne : 001078 ( Istex/Corpus ); précédent : 001077; suivant : 001079Conical algorithm for the global minimization of linearly constrained decomposable concave minimization problems
Auteurs : R. Horst ; N. V. ThoaiSource :
- Journal of Optimization Theory and Applications [ 0022-3239 ] ; 1992-09-01.
Abstract
Abstract: In this paper, we are concerned with the linearly constrained global minimization of the sum of a concave function defined on ap-dimensional space and a linear function defined on aq-dimensional space, whereq may be much larger thanp. It is shown that a conical algorithm can be applied in a space of dimensionp + 1 that involves only linear programming subproblems in a space of dimensionp +q + 1. Some computational results are given.
Url:
DOI: 10.1007/BF00940322
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<front><div type="abstract" xml:lang="en">Abstract: In this paper, we are concerned with the linearly constrained global minimization of the sum of a concave function defined on ap-dimensional space and a linear function defined on aq-dimensional space, whereq may be much larger thanp. It is shown that a conical algorithm can be applied in a space of dimensionp + 1 that involves only linear programming subproblems in a space of dimensionp +q + 1. Some computational results are given.</div>
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<ArticleTitle Language="En">Conical algorithm for the global minimization of linearly constrained decomposable concave minimization problems</ArticleTitle>
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<ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>R.</GivenName>
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<Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>N.</GivenName>
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<FamilyName>Thoai</FamilyName>
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<Affiliation ID="Aff1"><OrgDivision>Fachbereich IV-Mathematik</OrgDivision>
<OrgName>University of Trier</OrgName>
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<Country>Germany</Country>
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<Affiliation ID="Aff2"><OrgName>Institute of Mathematics</OrgName>
<OrgAddress><City>Hanoi</City>
<Country>Vietnam</Country>
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<Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading>
<Para>In this paper, we are concerned with the linearly constrained global minimization of the sum of a concave function defined on a<Emphasis Type="Italic">p</Emphasis>
-dimensional space and a linear function defined on a<Emphasis Type="Italic">q</Emphasis>
-dimensional space, where<Emphasis Type="Italic">q</Emphasis>
may be much larger than<Emphasis Type="Italic">p</Emphasis>
. It is shown that a conical algorithm can be applied in a space of dimension<Emphasis Type="Italic">p</Emphasis>
+ 1 that involves only linear programming subproblems in a space of dimension<Emphasis Type="Italic">p</Emphasis>
+<Emphasis Type="Italic">q</Emphasis>
+ 1. Some computational results are given.</Para>
</Abstract>
<KeywordGroup Language="En"><Heading>Key Words</Heading>
<Keyword>Global optimization</Keyword>
<Keyword>concave minimization</Keyword>
<Keyword>conical algorithms</Keyword>
<Keyword>branch-and-bound methods</Keyword>
<Keyword>decomposition</Keyword>
</KeywordGroup>
<ArticleNote Type="CommunicatedBy"><SimplePara>Communicated by M. Avriel</SimplePara>
</ArticleNote>
<ArticleNote Type="Misc"><SimplePara>This research was accomplished while the second author was a Fellow of the Alexander von Humboldt Foundation, University of Trier, Trier, Germany.</SimplePara>
</ArticleNote>
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<abstract lang="en">Abstract: In this paper, we are concerned with the linearly constrained global minimization of the sum of a concave function defined on ap-dimensional space and a linear function defined on aq-dimensional space, whereq may be much larger thanp. It is shown that a conical algorithm can be applied in a space of dimensionp + 1 that involves only linear programming subproblems in a space of dimensionp +q + 1. Some computational results are given.</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">1992-09-01</dateIssued>
<copyrightDate encoding="w3cdtf">1992</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>
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<extent unit="pages"><start>469</start>
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