桂林电子科技大学最优化方法试题A卷

A卷试题：一、Determinewhetherthefollowingstatementsaretrueornot,andmarktheletter‘T’inthebracketifthestatementistrue,orelsemarktheletter‘F’.（5315points）1.Theset22,12Dxyxyisaconvexset（凸集）.()2.Thefunction222,,234fxyzxyzyzisstrictlyconvex.（严格凸）()3.Foralinearprogramming,ifthefeasibleregionisnonempty,thentheremustexistatleastoneoptimalsolution.()对于线性规划,如果可行域是非空的,那么必须至少存在一个最优解。4.Foralinearprogramming,anyoptimalsolutionisalsoanextremepointoffeasibleregion.()对于线性规划,任何最优解也是一个极点的可行域。5.Forthemethodofsteepestdescent,thetwoconsecutivesearchdirectionsareorthogonalmutually.()对于最速下降法,连续两个搜索方向相互正交。二、Writethedualforeachofthefollowingprimalproblems（10points）（写出每个下列原始的双重问题）(P1)123123123123max678..2202310,,0zxxxstxxxxxxxxx(P2)12121212min811..23245,0zxxstxxxxxx三、Usethesimplexalgorithmtosolvethefollowinglinearprogramming.（20points）（用简单算法解决下列线性规划。）123123123max53..36536150,1,2,3iSxxxstxxxxxxxi四、Fortheproblem11min,,fxxab,formulatethegoldensectionalgorithm.（15points）（对于这个问题,制定黄金分割算法）五、Considertheproblem332122111min833fxxxxx,computethegradientfxandHessian2fx,andfindthelocaloptimalsolutions.(20points)（考虑这个问题.......,计算梯度...和黑森...,和找到局部最优解）六、ConsidertheproblemDeterminewhetherthepoint11TisaK-Tpoint.（20points）22122112212min2..00fxxxstgxxxgxxx