中山大学数学建模讲座

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1、优化模型-数学建模华南理工大学理学院数学系刘深泉教授ExperimentalMathematicsComputerFormulaforPiIn1996,aPSLQprogramdiscoveredthisformulaforpi:Indeed,thisformulapermitsonetodirectlycalculatebinaryorhexadecimal(base-16)digitsofbeginningatanarbitrarystartingpositionn,withoutneedingtocal

2、culateanyofthefirstn-1digits.SrinivasaRamanujanOptimization-mathematicalprogrammingchoosingthebestelementfromsomesetofavailablealternativesLinearprogrammingIntegerprogramming.QuadraticprogrammingNonlinearprogramming.ConvexprogrammingSemidefiniteprogrammingSto

3、chasticprogramming.Robustprogramming..Combinatorialoptimization.Infinite-dimensionaloptimizationHeuristicalgorithmsConstraintsatisfactionOptimalcontrol.Dynamicprogramming.Mathematicalprogramming序数理论，选择理论一般最优化问题最优化问题的约束数学模型ComputationaloptimizationtechniquesSi

4、nglevariablesOptimizationMultivariablesOptimization优化算法1.Dijkstra算法，2.最小生成树Prim算法，3.最小费用，4.遗传算法算法复杂性，P，NP问题，NPC1000000$FinalSubmissionCountdownNetflix公司-成立于1997年的美国最大的在线DVD租赁商ContributedbyLesterMackeyOnlysixteenminutesremainedinthe$1millionNetflixPrizecompeti

5、tionwhenIhandedoverthefinalsetofpredictionstotheEnsembleteamcaptain.Themembersofournewlymintedteamhadbeenworkingfuriouslythroughthenight,hopingtoimproveuponourpreviousday’sscoreof.8554.Itwashardtobelievethatjusttwenty-fourhoursagowehadpassedthefour-teamcoalit

6、ionthathadoccupiedthefirstplacespotforthelast29days.Therewaslittletimetocelebrate;thepreviousleaderswouldnotgodownwithoutafight,sowehadtobereadywithsomethingbetter.Acallhadbeenissuedforanyremainingvalidpredictors,anythingthatcouldtipthescaleinthisfinalday,and

7、ourmembersaroundtheglobehadansweredthecall:nearly200newpredictorsets,somepreviouslypassedoverfortheirpoorperformanceandothersnewlyconceivedonlymomentsprior,hadfloodedinfromallcornersoftheteam.Itwasnowuptoourblenderstoworksomelast-minutemagic.数学建模十大算法蒙特卡罗算法、数据

8、插值拟合、参数估计、层次分析法、线性规划问题图论算法、动态规划、回溯搜索、分治算法、分支定界等算法最优化理论的三大非经典算法：模拟退火法、神经网络、遗传算法CrystalBall——蒙地卡罗仿真软件Crystal Ball是Microsoft Excel的增益工具，采用Monte Carol仿真功能协助您分析风险与不确定模型。功能包含敏感度分析、相关性分析、tornado