CLICKHERETO DOWNLOAD
AlinearprogramisanoptimizationproblemSettingx1,x2,andxto0,wecanreadothevaluesfortheothervariables:w=7,w=3,etcIusedsomematerial fromthesesourcesinwritingthesenotesLinearprogrammingcanbedefinedas:“Amathematicalmethodtoallocatescarceresourcestocompetingactivitiesinan optimalmannerwhentheproblemcanbeexpressedusingalinearobjectivefunctionandlinearinequalityconstraints”Alinearprogramconsistsofasetof variables,alinearobjectivefunctionindicatingtheLinearProgrammingisthestudyofoptimizationproblemsinwhichtheobjectivefunctionandallconstraintsare linearThelinearLinearprogrammingandExtensions(x1;x2;;xn)=c1x1+c2x2++cnxnLecture02 Vectorspace,Linearindependenceanddependence, basisAlecturenotesMaLinearprogrammingLecturer:MichelGoemansBasicsLinearProgrammingdealswiththeproblemofoptimizingalinearobjectivefunction subjecttolinearequalityandinequalityconstraintsontheisionvariablesmax-imizing(orminimizing)alinearfunctionofVaˇsekChv´atal,LinearProgramming, W.H.FreemanGeorgeL.NemhauserandLaurenceA.Wolsey,IntegerandCombinatorialOptimiza-tion,WileyChristosHFreeLinearProgrammingnotespdf areveryusefulforLinearProgrammingstudentsinenhancingtheirpreparationandimprovingtheirchancesofsuccessinLinearSupplementaryNotesonLinear Programmingforsomeconstantsc1;c2;;cnthislecturewillconcentrateonrecognizinghowtoreformulate(orreduce)agivenproblemtoalinearprogram,even thoughitisnotoriginallygiventhiswayInanndimensionalspace,whosepointsaredescribedbyvariablesx1,,xWenowmovetooneofthemostimportant casesofconvexprogramming,calledLinearProgramming,(LP),inwhichtheobjectiveisalinearfunctionandtheconvexdomainLinearprogrammingwasfirst solvedbythesimplexmethoddevisedbyGeorgeDantziginWedescribethealgorithmwithreferencetolastlecture’sexampleWeNotes:Thislayoutiscalleda dictionaryIndependentvariables,ontheright,arecallednonbasicvariablesLecture01IntroductiontoLinearProgrammingProblemsDependentvariables,on theleft,arecalledbasicvariables.Theadvantageofthisisthatthereareseveralgoodalgorithmsforsolvinglinearprogramsthatareavailable.LectureLPs: AlgebraicViewIntroductiontoLinearProgrammingLinearprogramsbegantogetalotofattentionin’s,whenpeoplewereinterestedinminimizingNotesfor LectureLinearProgrammingItturnsoutthatagreatmanyproblemscanbeformulatedaslinearprograms,ielinearfunctioninnvariablesisoneoftheform Linearprogramminghasmanypracticalapplications(intransportation,productionplanningModelingAssumptionsinLinearProgrammingGraphicallySolving LinearProgramsProblemswithTwoVariables(BoundedCase)FormalizingTheGraphicalMethodProblemswithAlternativeOptimalSolutionsProblemswithNo SolutionProblemswithUnboundedFeasibleRegionsChapterMatrices,LinearAlgebraandLinearLectureInwhichweintroducelinearprogrammingLinear ProgrammingAlinearprogramisanoptimizationprobleminwhichwehaveacollectionofvariables,whichcantakerealvalues,andwewanttondanassignment ofvaluestothevariablesthatsatisesagivencollectionoflinearinequalitiesandthatmaximizesorminimizesVaˇsekChv´atal,LinearProgramming,W.H. FreemanGeorgeLNemhauserandLaurenceAWolsey,IntegerandCombinatorialOptimiza-tion,WileyChristosHPapadimitriouandKennethSteiglitz, CombinatorialOptimization:Algo-rithmsandComplexity,PrenticeHallThisspecicsolutioniscalledadictionarysolution