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Convergence of the steepest descent method for minimizing quasiconvex functions

dc.contributor.authorKiwiel, K. C.en_US
dc.contributor.authorMurty, Katta G.en_US
dc.date.accessioned2006-09-11T15:50:34Z
dc.date.available2006-09-11T15:50:34Z
dc.date.issued1996-04en_US
dc.identifier.citationKiwiel, K. C.; Murty, K.; (1996). "Convergence of the steepest descent method for minimizing quasiconvex functions." Journal of Optimization Theory and Applications 89(1): 221-226. <http://hdl.handle.net/2027.42/45245>en_US
dc.identifier.issn1573-2878en_US
dc.identifier.issn0022-3239en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/45245
dc.description.abstractTo minimize a continuously differentiable quasiconvex function f : ℝ n →ℝ, Armijo's steepest descent method generates a sequence x k +1 = x k − t k ∇ f ( x k ), where t k >0. We establish strong convergence properties of this classic method: either , s.t. ; or arg min f = ∅, ∥ x k ∥ ↓ ∞ and f(x k )↓ inf f . We also discuss extensions to other line searches.en_US
dc.format.extent204438 bytes
dc.format.extent3115 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.language.isoen_US
dc.publisherKluwer Academic Publishers-Plenum Publishers; Plenum Publishing Corporation ; Springer Science+Business Mediaen_US
dc.subject.otherTheory of Computationen_US
dc.subject.otherOptimizationen_US
dc.subject.otherCalculus of Variations and Optimal Controlen_US
dc.subject.otherOptimizationen_US
dc.subject.otherOperations Research/Decision Theoryen_US
dc.subject.otherConvex Programmingen_US
dc.subject.otherEngineering, Generalen_US
dc.subject.otherSteepest Descent Methodsen_US
dc.subject.otherArmijo's Line Searchen_US
dc.subject.otherMathematicsen_US
dc.subject.otherApplications of Mathematicsen_US
dc.titleConvergence of the steepest descent method for minimizing quasiconvex functionsen_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, University of Michigan, Ann Arbor, Michiganen_US
dc.contributor.affiliationotherSystems Research Institute, Warsaw, Polanden_US
dc.contributor.affiliationumcampusAnn Arboren_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/45245/1/10957_2005_Article_BF02192649.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1007/BF02192649en_US
dc.identifier.sourceJournal of Optimization Theory and Applicationsen_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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