桂林电子科技大学最优化方法试题B卷

B卷试题：一、Determinewhetherthefollowingstatementsaretrueornot,andmarktheletter‘T’inthebracketifthestatementistrue,orelsemarktheletter‘F’.（5420points）1.Theconvexset22,10Dxyxyhasnoextremepoints.()凸集……没有极端点2.Thefunction222,,234fxyzxyzyzisconcave.()函数。。。。是凹的3.Forlinearprogrammingproblem,thedualisinfeasiblewhentheprimalisunbounded.()线性规划问题的对偶是不可行,原始的是无限的4.Forthelinearprogrammingproblem,anybasicfeasiblesolutionisalsoanextremepointofthefeasibleregion.()任何基本可行解的线性规划问题,也是一个极端点的可行域5.Forthemethodofsteepestdescent,thetwoconsecutivesearchdirectionsareorthogonalmutually.()最陡下降法,连续两个搜索方向相互正交二、Considerthefollowinglinearprogrammingproblem（考虑下面的线性规划问题）Itisknownthat134,,xxxareoptimalbasicvariables,writeoutthecorrespondingoptimalsimplextableau.（众所周知......是最优基变量,写出相应的最优单纯形表）(20points)三、UsethedualsimplexmethodtosolvethefollowingLP（用对偶单纯形法解决以下线性规划问题）123123123min234..232340SxxxstxxxPxxxx(20points)四、Let222123231232224662fxxxxxxxxxandassume（假设）fxcanberewritedas（可以重写为）12TfxxAxbxc,TAA,then1）findout,Abandc2）Evaluate（求....的值）fxand2fx3）solvetheproblemminfx（20points）五、Usethesteepestdescendmethodtosolvethefollowingproblem.（使用最速下降法来解决以下问题）221212min,32fxxxxBeginatthepoint111xandthetolerance0.（公差0）（20points）