桂林电子科技大学最优化方法A卷答案

A卷答案：一、（5315分）1--5：FTFFT二、Writethedualforeachofthefollowingprimalproblems(P1)123123123123max678..2202310,,0zxxxstxxxxxxxxx(P2)12121212min811..23245,0zxxstxxxxxxSolution:(D1)1212121212min2010..2627380,unrestrictedwyystyyyyyyyy（5分）(D2)12121212max35..2824110,0wyystyyyyyy（5分）三、(满分20分)Solution：Itsstandardformisas（它的标准形式）12312341235max53..36536150,1,2,3iSxxxstxxxxxxxxxi(4分)andtheinitialsimplextableauis（和初始单纯形表为）X1X2X3X4X5RHSX4113106X55360115S-5-3-1000(4分)ThenwehaveX1X2X3X4X5RHSX402/59/51-1/53X113/56/501/53S0050115300,or30030,*15TTxxS(4分)andX1X2X3X4X5RHSX4-2/3011-1/151X25/31201/35S0050115050,or05010,*15TTxxS(4分)Therefore,thegeneralsolutionscanbeexpressedas:（因此,一般的解决方案可以表示为）*1,0,1xxx(4分)四、(满分15分)Solution：Step1:select11,abastheinitialintervalandgiveatolerance0andlet1k;（2分）（选择........作为初始间隔和给出公差.......和让.........）Step2:let0.382,0.618kkkkkkkkabaabaandevaluate（求...的值）fxatkandk;（4分）Step3:ifkkff,set11,kkkkabb,otherwise,set11,kkkkaab;（4分）Step4:if11kkba,stoptheiteration（停止迭代）.Theoptimalsolution*kxwhenkkff,orelse*kx;（3分）Step5:if11kkba,thenset1kk,andturntostep2;（2分）五、Solution:accordingtotheproblem,wehave2122212xfxxx,12220022xfxx（5分）Let0fx,i.e.212221020xxxSolvetheequationssetandweobtainfourstationarypointsasfollows:（解方程组和我们获得四个驻点如下）10,12,10,12TTTT（5分）ComputingtheHessianmatrixatthesefourpointsyields（在这四个点计算海赛矩阵产量）2201002f,2201202f2201002f,2201202f（5分）Wecanseeonly22012002f,hence12Tisanlocaloptimalsolution.（局部最优解）（5分）