lecture01 - Yinyu Ye MS&E Stanford MS&E211 Lecture...

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Unformatted text preview: Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #01 1 LinearandNonLinearProgramming YinyuYe DepartmentofManagementScienceandEngineering StanfordUniversity Stanford,CA94305,U.S.A. http://www.stanford.edu/˜yyye Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #01 2 IntroductiontoOptimization Anyscenarioinwhichyouaretryingtomakecertaindecisionsandreachthebest possibleoutcome. Optimization isthecommongoalof ManagementScienceand Engineering . Optimizationisconcernedwiththestudyof maximizationandminimizationof mathematicalfunctions. Veryoftentheargumentsof(i.e., variables or unknowns in)thesefunctionsaresubjecttosideconditionsor constraints. Byvirtueofits greatutilityinsuchdiverseareasasappliedscience,engineering,economics, finance,medicine,andstatistics,optimizationholdsanimportantplaceinthe practicalworldandthescientificworld.Indeed,asfarbackastheEighteenth Century,thefamousSwissmathematicianandphysicistLeonhardEuler (1707-1783)proclaimed a that ...nothingatalltakesplaceintheUniversein whichsomeruleofmaximumorminimumdoesnotappear. a SeeLeonhardoEulero, MethodusInviendiLineasCurvasMaximiMinimiveProprietateGaudentes , Lausanne&Geneva,1744,p.245. Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #01 3 WheredoOptimizationProblemscomefrom? • Economics :Consumertheory/suppliertheory • Finance :Optimalhedging/pricing • Science/Engineering :Aerospace,productdesign,datamining • OtherBusinessdecisions :scheduling,production,organizationaldecisions • Government :Militaryapplications,fundallocation,etc • OtherPersonaldecisions :Sports,on-fielddecisions,playeracquisition, marketing Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #01 4 QuantitativeorMathematicalModels Theclassofoptimizationproblemsconsideredinthiscoursecanallbeexpressed intheform (P) minimize f ( x ) subjectto x ∈X where X usuallyspecifiedbyconstraints: c i ( x )= i ∈E c i ( x ) ≤ i ∈I . Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #01 5 ProductionManagement TheWyndorGlassCo.isaproducerofhigh-qualityglass products .Ithasthree plans .AluminumframesandhardwarearemadeinPlant1,woodframesare madeinPlant2,andPlant3isusedtoproduceglassandassembletheproducts. Wyndorproducestoproductswhichrequirethe resources ofthe2plantsas follows: Plant Aluminum Wood Resources 1 1 100 2...
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This note was uploaded on 06/16/2010 for the course MS&E 211 taught by Professor Yinyuye during the Fall '07 term at Stanford.

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lecture01 - Yinyu Ye MS&E Stanford MS&E211 Lecture...

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