Optimization第一讲-IntroductionVIP免费

FacultyofEconomicsOptimizationLecture1MarcoHaanFebruary14,2005第一页，共三十九页。Introduction•ThisisamathcourseforAEstudents.•Theemphasisonapplications.•Thegoalistoprovideyouwiththemathematicalskillsrequiredforthemoreadvancedcourses,especiallyinmicroandmacro.•Literature:Hoy,Livernois,McKenna,Rees,StengosMathematicsforEconomics,MIT-Press,2ndedition,2001.•Forthosewhotookthiscourselastyear:thisbookisinfinitelybetterthanLambert.•Forthiscourse,practiceisessential!!!•Note:thereisaSolutionsManualforthisbook,withsolutionsforallodd-numberedproblems.2第二页，共三十九页。Introduction•ThisisamathcourseforAEstudents.•Theemphasisonapplications.•Thegoalistoprovideyouwiththemathematicalskillsrequiredforthemoreadvancedcourses,especiallyinmicroandmacro.•Literature:Hoy,Livernois,McKenna,Rees,StengosMathematicsforEconomics,MIT-Press,2ndedition,2001.•Forthosewhotookthiscourselastyear:thisbookisinfinitelybetterthanLambert.•Forthiscourse,practiceisessential!!!•Note:thereisaSolutionsManualforthisbook,withsolutionsforallodd-numberedproblems.3第三页，共三十九页。Introduction(2)•TheTeam:•Dr.M.A.Haanm.a.haan@eco.rug.nl(micro,semester2a)•Prof.dr.E.Sterkene.sterken@eco.rug.nl(macro,semester2b)•Drs.L.Daml.dam@eco.rug.nl(exercisehours,entiresemester)•Classes:•selectedMondays,10:00-12:00,ZG114•selectedThursdays,15:00-17:00,ZG1074第四页，共三十九页。Set-up•Lectures,exercisehours,take-home,exam.•Onelectureperweek.Oneexercisemeetingperweek.•Exercisestobediscussedwillbeannouncedinadvance.•Dotheexercisesbeforethemeeting!!!•Therewillbe3take-homeproblemsets.•Youhaveroughlytwoweeksforeach.•Duringthesetwoweeks,therewillbeno(orfewer)lectures.•Problemsetswillberelativelytough.•Youcandiscusswithothers,butyoucannotcooperate.•Ifyoudo,wewillfindout.•Withthesets,youcanearn2bonuspointsonyourfinalgrade.•Thebonuspointsarelikelytobecrucial.•AllyouneedwillbeonNestor.5第五页，共三十九页。PreliminaryScheduleFeb14Optimizationwithn-variables(H12)Feb17ExercisesH12Feb21ConstrainedOptimization(H13)Feb24ExercisesH13Feb28ComparativeStatics(H14)Mar3ExercisesH14Mar7ConcaveProgramming(H15)Mar10NoclassProblemSet1distributedMar14NoclassMar17NoclassMar21NoclassMar24NoclassProblemset1dueMar28EASTERN(noclass)Mar31ExercisesH15Apr4Integration(H16)Apr7ExercisesH16ProblemSet2distributed6第六页，共三十九页。PreliminarySchedule(cont’d)May2DifferenceEquations(H18-20)May5ASCENS’NDAY(noclass)Problemset2dueMay9DifferentialEquations(H21-23)May12ExercisesH18-20May16PENTECOST(noclass)May19ExercisesH21-23May23SystemsofDiffEquations(H24)May26ExercisesH24May30DynamicOptimization1(H25)June2ExercisesH251ProblemSet3distributedJune6NoclassJune9NoclassJune13DynamicOptimization2(H25)June16ExercisesH252June20DynamicOptimization3(add)June23ExercisesadditionalProblemset3dueJuly14Exam7第七页，共三十九页。Today:Chapter121.Concavity.2.Stationaryvalues.3.Localoptima.4.Secondorderconditions.5.Directrestrictionsonvariables.6.Shadowprices.7.Note:IntheselecturesIwillfocusonthemainideasandintuition.8.Definitionsandtheoremsareinthebook.8第八页，共三十九页。ConcavityThefunctionfisconcaveif1212((1))()(1)()fxxfxfxforallλin[0,1].Itisstrictlyconcaveifthestrictinequalityholdsforallλin[0,1].Whatthissaysis:1.Takeanytwopointsonthegraph.2.Drawalinebetweenthosepoints.3.Theentirelineshouldbebelowthegraph.Ifthesecondderivativeisne...