An algorithmic proof of the polyhedral decomposition theorem

dc.citation.epage472en_US
dc.citation.spage463en_US
dc.citation.volumeNumber35en_US
dc.contributor.authorAkgül, M.en_US
dc.date.accessioned2019-02-19T11:33:28Z
dc.date.available2019-02-19T11:33:28Z
dc.date.issued1988en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractIt is well‐known that any point in a convex polyhedron P can be written as the sum of a convex combination of extreme points of P and a non‐negative linear combination of extreme rays of P. Grötschel, Lovász, and Schrijver gave a polynomial algorithm based on the ellipsoidal method to find such a representation for any x in P when P is bounded. Here we show that their algorithm can be modified and implemented in polynomial time using the projection method or a simplex‐type algorithm : in n(2n + 1) simplex pivots, where n is the dimension of x. Extension to the unbounded case is immediate.en_US
dc.description.provenanceSubmitted by Merve Nalbant (merve.nalbant@bilkent.edu.tr) on 2019-02-19T11:33:28Z No. of bitstreams: 1 An_algorithmic_proof_of_the_polyhedral_decomposition_theorem.pdf: 515715 bytes, checksum: f346c594466f2c89703799920fab3fba (MD5)en
dc.description.provenanceMade available in DSpace on 2019-02-19T11:33:28Z (GMT). No. of bitstreams: 1 An_algorithmic_proof_of_the_polyhedral_decomposition_theorem.pdf: 515715 bytes, checksum: f346c594466f2c89703799920fab3fba (MD5) Previous issue date: 1988en
dc.identifier.issn0894-069X (print)
dc.identifier.issn1520-6750 (online)
dc.identifier.urihttp://hdl.handle.net/11693/49599
dc.language.isoEnglishen_US
dc.publisherJohn Wiley & Sonsen_US
dc.source.titleNaval Research Logisticsen_US
dc.titleAn algorithmic proof of the polyhedral decomposition theoremen_US
dc.typeArticleen_US

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