Title of article
Column generationalgorithmsfornonlinearoptimization,II: Numericalinvestigations
Author/Authors
Ricardo Garc?´a-Ro´ denas ، نويسنده , , AngelMar?´nb، نويسنده , , MichaelPatriksson ، نويسنده ,
Issue Information
ماهنامه با شماره پیاپی سال 2011
Pages
14
From page
591
To page
604
Abstract
Garcı´a etal. [1] presentaclassofcolumngeneration(CG)algorithmsfornonlinearprograms.Itsmain
motivationfromatheoreticalviewpointisthatundersomecircumstances,finiteconvergencecanbe
achieved,inmuchthesamewayasfortheclassicsimplicialdecompositionmethod;themainpractical
motivationisthatwithintheclasstherearecertainnonlinearcolumngenerationproblemsthatcan
acceleratetheconvergenceofasolutionapproachwhichgeneratesasequenceoffeasiblepoints.This
algorithmcan,forexample,acceleratesimplicialdecompositionschemesbymakingthesubproblems
nonlinear.Thispapercomplementsthetheoreticalstudyontheasymptoticandfiniteconvergenceof
these methodsgivenin [1] with anexperimentalstudyfocusedontheircomputationalefficiency.
Three typesofnumericalexperimentsareconducted.Thefirstgroupoftestproblemshasbeen
designedtostudytheparametersinvolvedinthesemethods.Thesecondgrouphasbeendesignedto
investigatetheroleandthecomputationoftheprolongationofthegeneratedcolumnstotherelative
boundary.Thelastonehasbeendesignedtocarryoutamorecompleteinvestigationofthedifference
in computationalefficiencybetweenlinearandnonlinearcolumngenerationapproaches.
In ordertocarryoutthisinvestigation,weconsidertwotypesoftestproblems:thefirstoneisthe
nonlinear,capacitatedsingle-commoditynetworkflowproblemofwhichseverallarge-scaleinstances
with varieddegreesofnonlinearityandtotalcapacityareconstructedandinvestigated,andthesecond
one isacombinedtrafficassignmentmodel.
Keywords
Network flow problems , Simplicial decomposition , Nonlinear column generation , Convex minimization
Journal title
Computers and Operations Research
Serial Year
2011
Journal title
Computers and Operations Research
Record number
927884
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