Projected Newton methods and optimization of multicommodity flows

A superlinearly convergent Newton like method for linearly constrained optimization problems is adapted for solution of multicommodity network flow problems of the type arising in communication and transportation networks. We show that the method can be implemented approximately by making use of con...

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Veröffentlicht in:	IEEE transactions on automatic control 1983-12, Vol.28 (12), p.1090-1096
Hauptverfasser:	Bertsekas, D., Gafni, E.
Format:	Artikel
Sprache:	eng
Schlagworte:	communications Computer science Constraint optimization Convergence Equations flow networks Newton method operations research optimization Optimization methods Proposals Quadratic programming Transportation
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container_title	IEEE transactions on automatic control
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creator	Bertsekas, D. Gafni, E.
description	A superlinearly convergent Newton like method for linearly constrained optimization problems is adapted for solution of multicommodity network flow problems of the type arising in communication and transportation networks. We show that the method can be implemented approximately by making use of conjugate gradient iterations without the need to compute explicitly the Hessian matrix. Preliminary computational results suggest that this type of method is capable of yielding highly accurate solutions of nonlinear multicommodity flow problems far more efficiently than any of the methods available at present.
doi_str_mv	10.1109/TAC.1983.1103183
format	Article
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We show that the method can be implemented approximately by making use of conjugate gradient iterations without the need to compute explicitly the Hessian matrix. Preliminary computational results suggest that this type of method is capable of yielding highly accurate solutions of nonlinear multicommodity flow problems far more efficiently than any of the methods available at present.</description><subject>communications</subject><subject>Computer science</subject><subject>Constraint optimization</subject><subject>Convergence</subject><subject>Equations</subject><subject>flow</subject><subject>networks</subject><subject>Newton method</subject><subject>operations research</subject><subject>optimization</subject><subject>Optimization methods</subject><subject>Proposals</subject><subject>Quadratic programming</subject><subject>Transportation</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1983</creationdate><recordtype>article</recordtype><recordid>eNqFkEtLAzEUhYMoWKt7wc2sdDU172SWpfiCoi7qOuQ1mDLT1ElKqb_elBbc6epyON-593IAuEZwghBs7hfT2QQ1kuwVQZKcgBFiTNaYYXIKRhAiWTdY8nNwkdKySE4pGoHp-xCX3mbvqle_zXFV9T5_RpcqvXJVXOfQh2-dQzFiW_WbLgcb-z66kHdV28VtugRnre6SvzrOMfh4fFjMnuv529PLbDqvLWEs11QQ43ljjMBNa7iDQlCChICNk8ZCiBtIpNFUeEGdtgxi4SwVGkFryreOjMHdYe96iF8bn7LqQ7K-6_TKx01SgjLOOYWwkLd_kuUUYoiR_0HJMOIcFxAeQDvElAbfqvUQej3sFIJqX78q9at9_epYf4ncHCLBe_-LH90fKOmAAg</recordid><startdate>19831201</startdate><enddate>19831201</enddate><creator>Bertsekas, D.</creator><creator>Gafni, E.</creator><general>IEEE</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>H8D</scope><scope>7TC</scope></search><sort><creationdate>19831201</creationdate><title>Projected Newton methods and optimization of multicommodity flows</title><author>Bertsekas, D. ; Gafni, E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-473be69bb729fb6d0774317709d8bc0029038ba47e74dac5027dc47a10cb001d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1983</creationdate><topic>communications</topic><topic>Computer science</topic><topic>Constraint optimization</topic><topic>Convergence</topic><topic>Equations</topic><topic>flow</topic><topic>networks</topic><topic>Newton method</topic><topic>operations research</topic><topic>optimization</topic><topic>Optimization methods</topic><topic>Proposals</topic><topic>Quadratic programming</topic><topic>Transportation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bertsekas, D.</creatorcontrib><creatorcontrib>Gafni, E.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Aerospace Database</collection><collection>Mechanical Engineering Abstracts</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bertsekas, D.</au><au>Gafni, E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Projected Newton methods and optimization of multicommodity flows</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>1983-12-01</date><risdate>1983</risdate><volume>28</volume><issue>12</issue><spage>1090</spage><epage>1096</epage><pages>1090-1096</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>A superlinearly convergent Newton like method for linearly constrained optimization problems is adapted for solution of multicommodity network flow problems of the type arising in communication and transportation networks. We show that the method can be implemented approximately by making use of conjugate gradient iterations without the need to compute explicitly the Hessian matrix. Preliminary computational results suggest that this type of method is capable of yielding highly accurate solutions of nonlinear multicommodity flow problems far more efficiently than any of the methods available at present.</abstract><pub>IEEE</pub><doi>10.1109/TAC.1983.1103183</doi><tpages>7</tpages></addata></record>
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subjects	communications Computer science Constraint optimization Convergence Equations flow networks Newton method operations research optimization Optimization methods Proposals Quadratic programming Transportation
title	Projected Newton methods and optimization of multicommodity flows
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