实验报告11
实验名称：用MATLAB解二次型规划和一般非线性规划问题
实验目的：学会如何运用MATLAB解二次型规划和一般非线性规划问题； 实验内容：
书P211
11、试求解下面的二次型规划问题。
min2x1?4x1x2?4x2?6x1?3x2
?x1?x2?3?xs.t.?4x1?x2?9
?x?0?1,2解：
>> f=[-6,-3];H=[4,-4;-4,8];
>> A=[1,1;4,1];B=[3,9];Aeq=[];Beq=[];xm=zeros(2,1); >> [x,f_opt]=quadprog(H,f,A,B,Aeq,Beq,xm,[],[])
Warning: Your Hessian is not symmetric. Resetting H=(H+H')/2. > In quadprog at 232
Warning: Large-scale method does not currently solve this problem formulation, using medium-scale method instead. > In quadprog at 263 Optimization terminated. x =
1.9500 1.0500
f_opt =
-11.0250
12、试求解下面的非线性规划问题。
22minex14x1?2x2?4x1x2?2x2?1
?22?
x1?x2?0???xx?x?x?1.5?xs.t.?1212
x1x2??10????10?x1,x2?10解：
function [c,ceq]=cdd01(x)
c=[x(1)+x(2);x(1)*x(2)-x(1)-x(2)+1.5;-x(1)*x(2)-10];ceq=[];
>> y=@(x)exp(x(1))*(4*x(1)*x(1)+2*x(2)*x(2)+4*x(1)*x(2)+2*x(2)+1); x0=[1;1];xm=[-10;-10];xM=[10;10];A=[];B=[];Aeq=[];Beq=[]; [x,f_opt,c,d]=fmincon(y,x0,A,B,Aeq,Beq,xm,xM,@cdd01)
Warning: Trust-region-reflective method does not currently solve this type of problem, using active-set (line search) instead. > In fmincon at 422
Maximum number of function evaluations exceeded; increase OPTIONS.MaxFunEvals. x =
3.1740 -7.9967
f_opt =
1.2351e+003 c =
0 d =
iterations: 54 funcCount: 201 lssteplength: 1
stepsize: 5.6428
algorithm: 'medium-scale: SQP, Quasi-Newton, line-search' firstorderopt: 390.0759 constrviolation: 1.7857e-008 message: [1x79 char]
15、试求解下面的0-1线性规划问题
解
>> f=[5,7,10,3,1]
>> A=[-1,1,-5,-1,4;2,-6,3,2,-2;0,-2,2,-1,-1] >> B=[-2;0;1]
>> x_m=[0,0,0,0,0] >> x_M=[1,1,1,1,1]
>> x=bintprog(f,A,B,[],[],x_m,x_M) x =
0 1 1 0 0