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dc.contributor.authorSchochetman, Irwin E.en_US
dc.contributor.authorSmith, Robert L.en_US
dc.date.accessioned2006-09-11T19:33:27Z
dc.date.available2006-09-11T19:33:27Z
dc.date.issued1992-02en_US
dc.identifier.citationSchochetman, Irwin E.; Smith, Robert L.; (1992). "Finite dimensional approximation in infinite dimensional mathematical programming." Mathematical Programming 54 (1-3): 307-333. <http://hdl.handle.net/2027.42/47924>en_US
dc.identifier.issn0025-5610en_US
dc.identifier.issn1436-4646en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/47924
dc.description.abstractWe consider the problem of approximating an optimal solution to a separable, doubly infinite mathematical program (P) with lower staircase structure by solutions to the programs (P( N )) obtained by truncating after the first N variables and N constraints of (P). Viewing the surplus vector variable associated with the N th constraint as a state, and assuming that all feasible states are eventually reachable from any feasible state, we show that the efficient set of all solutions optimal to all possible feasible surplus states for (P( N )) converges to the set of optimal solutions to (P). A tie-breaking algorithm which selects a nearest-point efficient solution for (P( N )) is shown (for convex programs) to converge to an optimal solution to (P). A stopping rule is provided for discovering a value of N sufficiently large to guarantee any prespecified level of accuracy. The theory is illustrated by an application to production planning.en_US
dc.format.extent1418389 bytes
dc.format.extent3115 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.language.isoen_US
dc.publisherSpringer-Verlag; The Mathematical Programming Society, Inc.en_US
dc.subject.otherInfinite Horizon Optimizationen_US
dc.subject.otherStopping Ruleen_US
dc.subject.otherSolution Set Convergenceen_US
dc.subject.otherValue Convergenceen_US
dc.subject.otherProduction Planningen_US
dc.subject.otherReachabilityen_US
dc.subject.otherTie-breakingen_US
dc.subject.otherMathematical and Computational Physicsen_US
dc.subject.otherOptimizationen_US
dc.subject.otherCalculus of Variations and Optimal Controlen_US
dc.subject.otherCombinatoricsen_US
dc.subject.otherMathematical Methods in Physicsen_US
dc.subject.otherMathematics of Computingen_US
dc.subject.otherNumerical Analysisen_US
dc.subject.otherOperation Research/Decision Theoryen_US
dc.subject.otherMathematicsen_US
dc.subject.otherNumerical and Computational Methodsen_US
dc.titleFinite dimensional approximation in infinite dimensional mathematical programmingen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelMathematicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Industrial and Operations Engineering, The University of Michigan, 48109, Ann Arbor, MI, USAen_US
dc.contributor.affiliationotherDepartment of Mathematical Sciences, Oakland University, 48309, Rochester, MI, USAen_US
dc.contributor.affiliationumcampusAnn Arboren_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/47924/1/10107_2005_Article_BF01586057.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1007/BF01586057en_US
dc.identifier.sourceMathematical Programmingen_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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