Inexact primal-dual interior point iteration for linear programs in function spaces
Identifieur interne : 000C23 ( Istex/Corpus ); précédent : 000C22; suivant : 000C24Inexact primal-dual interior point iteration for linear programs in function spaces
Auteurs : S. Ito ; C. T. Kelley ; E. W. SachsSource :
- Computational Optimization and Applications [ 0926-6003 ] ; 1995-07-01.
Abstract
Abstract: Motivated by a simple optimal control problem with state constraints, we consider an inexact implementation of the primal-dual interior point algorithm of Zhang, Tapia, and Dennis. We show how the control problem can be formulated as a linear program in an infinite dimensional space in two different ways and prove convergence results.
Url:
DOI: 10.1007/BF01300870
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ISTEX:ED98E3F8AD47E538682731AEF5C7DF0C16BFD453Le document en format XML
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Ito</name><affiliation><mods:affiliation>Department of Prediction and Control, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, 106, Minato-ku, Tokyo, Japan</mods:affiliation></affiliation></author><author><name sortKey="Kelley, C T" sort="Kelley, C T" uniqKey="Kelley C" first="C. T." last="Kelley">C. T. Kelley</name><affiliation><mods:affiliation>Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Box 8205, 27695-8205, Raleigh, N.C.</mods:affiliation></affiliation></author><author><name sortKey="Sachs, E W" sort="Sachs, E W" uniqKey="Sachs E" first="E. W." last="Sachs">E. W. 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We show how the control problem can be formulated as a linear program in an infinite dimensional space in two different ways and prove convergence results.</div></front></TEI><istex><corpusName>springer</corpusName><author><json:item><name>S. Ito</name><affiliations><json:string>Department of Prediction and Control, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, 106, Minato-ku, Tokyo, Japan</json:string></affiliations></json:item><json:item><name>C. T. Kelley</name><affiliations><json:string>Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Box 8205, 27695-8205, Raleigh, N.C.</json:string></affiliations></json:item><json:item><name>E. W. Sachs</name><affiliations><json:string>FB IV-Mathematik, Universität Trier, D-54286, Trier, Federal Republic of Germany</json:string></affiliations></json:item></author><articleId><json:string>BF01300870</json:string><json:string>Art1</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Motivated by a simple optimal control problem with state constraints, we consider an inexact implementation of the primal-dual interior point algorithm of Zhang, Tapia, and Dennis. We show how the control problem can be formulated as a linear program in an infinite dimensional space in two different ways and prove convergence results.</abstract><qualityIndicators><score>4.904</score><pdfVersion>1.3</pdfVersion><pdfPageSize>450 x 677 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>346</abstractCharCount><pdfWordCount>4268</pdfWordCount><pdfCharCount>21609</pdfCharCount><pdfPageCount>13</pdfPageCount><abstractWordCount>53</abstractWordCount></qualityIndicators><title>Inexact primal-dual interior point iteration for linear programs in function spaces</title><refBibs><json:item><author><json:item><name>E Anderson</name></json:item><json:item><name>E Nash</name></json:item></author><host><author></author><title>Linear Programming in Infinite-Dimensional Spaces</title><publicationDate>1987</publicationDate></host><publicationDate>1987</publicationDate></json:item><json:item><author><json:item><name>R Dembo</name></json:item><json:item><name>S Eisenstat</name></json:item><json:item><name>T Steihaug</name></json:item></author><host><volume>19</volume><pages><first>400408</first></pages><author></author><title>Inexact Newton methods," SIAM J. Numer. Anal</title><publicationDate>1982</publicationDate></host><publicationDate>1982</publicationDate></json:item><json:item><host><author><json:item><name>A,S E1-Bakry</name></json:item><json:item><name>R,A Tapia</name></json:item><json:item><name>T Tsuchiya</name></json:item><json:item><name>Y Zhang</name></json:item></author><title>On the formulation of the primal-dual Newton interior-point method for nonlinear programming</title><publicationDate>1992-12</publicationDate></host></json:item><json:item><host><pages><last>16</last><first>7</first></pages><author><json:item><name>E Jarre</name></json:item><json:item><name>M,A Saunders</name></json:item></author><title>An adaptive primal-dual method for linear programming</title><publicationDate>1991</publicationDate></host></json:item><json:item><host><author><json:item><name>W Krabs</name></json:item></author><title>Optimierung und Approximation</title><publicationDate>1975</publicationDate></host></json:item><json:item><host><pages><last>257</last><first>245</first></pages><author><json:item><name>E Leibfritz</name></json:item><json:item><name>E,W Sachs</name></json:item></author><title>Numerical solution of parabolic state constrained control problmes using SQPand interior point methods," in Large Scale Optimization: State of the Art</title><publicationDate>1994</publicationDate></host></json:item><json:item><author><json:item><name>S,J Wright</name></json:item></author><host><volume>16</volume><pages><last>223</last><first>221</first></pages><author></author><title>Parallel Computing</title><publicationDate>1990</publicationDate></host><title>Solution of discrete-time optimal control problems on parallel computers</title><publicationDate>1990</publicationDate></json:item><json:item><author><json:item><name>S,J Wright</name></json:item></author><host><volume>77</volume><pages><last>174</last><first>161</first></pages><author></author><title>J, Optim. Theory Appl</title><publicationDate>1993</publicationDate></host><title>Interior point methods for optimal control of discrete-time systems</title><publicationDate>1993</publicationDate></json:item><json:item><author><json:item><name>Y Zhang</name></json:item><json:item><name>R,A Tapia</name></json:item><json:item><name>Le Dennis</name></json:item></author><host><volume>2</volume><pages><last>323</last><first>304</first></pages><author></author><title>SIAM J. Optimization</title><publicationDate>1992</publicationDate></host><title>On the supeflinear and quadratic convergence of primal-dual interior point linear programming algorithms</title><publicationDate>1992</publicationDate></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>4</volume><pages><last>201</last><first>189</first></pages><issn><json:string>0926-6003</json:string></issn><issue>3</issue><subject><json:item><value>Convex and Discrete Geometry</value></json:item><json:item><value>Optimization</value></json:item><json:item><value>Operations Research, Mathematical Programming</value></json:item><json:item><value>Statistics, general</value></json:item><json:item><value>Operation Research/Decision 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Tokyo</City><Country>Japan</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>Department of Mathematics, Center for Research in Scientific Computation</OrgDivision><OrgName>North Carolina State University</OrgName><OrgAddress><Postbox>Box 8205</Postbox><Postcode>27695-8205</Postcode><City>Raleigh</City><State>N.C.</State></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgDivision>FB IV-Mathematik</OrgDivision><OrgName>Universität Trier</OrgName><OrgAddress><Postcode>D-54286</Postcode><City>Trier</City><Country>Federal Republic of Germany</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Motivated by a simple optimal control problem with state constraints, we consider an inexact implementation of the primal-dual interior point algorithm of Zhang, Tapia, and Dennis. We show how the control problem can be formulated as a linear program in an infinite dimensional space in two different ways and prove convergence results.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>state constrained optimal control problem</Keyword><Keyword>primal-dual interior point algorithm</Keyword><Keyword>linear programming</Keyword><Keyword>inexact Newton method</Keyword></KeywordGroup><KeywordGroup Language="En"><Heading>AMS(MOS) subject classification</Heading><Keyword>49M15</Keyword><Keyword>65H10</Keyword><Keyword>65K10</Keyword><Keyword>90C06</Keyword></KeywordGroup><ArticleNote Type="Misc"><SimplePara>The research of this author was supported by an Overseas Research Scholarship of the Ministry of Education, Science and Culture of Japan.</SimplePara></ArticleNote><ArticleNote Type="Misc"><SimplePara>The research of this author was supported by National Science Foundation grants #DMS-9024622 and #DMS-9321938, North Atlantic Treaty Organization grant #CRG 920067, and an allocation of computing resources from the North Carolina Supercomputing Program.</SimplePara></ArticleNote><ArticleNote Type="Misc"><SimplePara>The research of this author was supported by North Atlantic Treaty Organization grant #CRG 920067.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Inexact primal-dual interior point iteration for linear programs in function spaces</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Inexact primal-dual interior point iteration for linear programs in function spaces</title></titleInfo><name type="personal"><namePart type="given">S.</namePart><namePart type="family">Ito</namePart><affiliation>Department of Prediction and Control, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, 106, Minato-ku, Tokyo, Japan</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="given">T.</namePart><namePart type="family">Kelley</namePart><affiliation>Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University, Box 8205, 27695-8205, Raleigh, N.C.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">E.</namePart><namePart type="given">W.</namePart><namePart type="family">Sachs</namePart><affiliation>FB IV-Mathematik, Universität Trier, D-54286, Trier, Federal Republic of 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">Boston</placeTerm></place><dateCreated encoding="w3cdtf">1993-03-12</dateCreated><dateIssued encoding="w3cdtf">1995-07-01</dateIssued><copyrightDate encoding="w3cdtf">1995</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: Motivated by a simple optimal control problem with state constraints, we consider an inexact implementation of the primal-dual interior point algorithm of Zhang, Tapia, and Dennis. 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