利用matlab 求解非线性规划问题

利用matlab 求解非线性规划问题，其运行代码编写，可以这样来考虑：

1、创建目标函数，myobj(x)

f=-(2*x1+3*x1^2+3*x2+x2^2+x3)

2、创建约束条件函数，mycon(x)

根据给出的条件，来写不等式条件和等式条件

3、使用fmincon（）函数，求解x1，x2，x3。即

[x,fval,exitflag]=fmincon(@myobj,x0,[],[],[],[],lb,ub,@mycon)

这里，x0—初值，lb,ub—xi的上下限

4、得到x1，x2，x3，进行验证是否满足约束条件

function example()

options=optimset('largescale','off')

[x,y]=fmincon(@fun1,rand(1,3),[],[],[],[],zeros(1,3),[],@fun2,options)

function f=fun1(x)

f=sum(x.^2)+8

function [g,h]=fun2(x)

g=[-x(1)^2+x(2)-x(3)^2

x(1)+x(2)^2+x(3)^3-20]

h=[-x(1)-x(2)^2+2

x(2)+2*x(3)^2-3]

结果

Warning: Options LargeScale = 'off' and Algorithm =

'trust-region-reflective' conflict.

Ignoring Algorithm and running active-set algorithm. To run

trust-region-reflective, set

LargeScale = 'on'. To run active-set without this warning, use

Algorithm = 'active-set'.

>In fmincon at 445

In example at 3

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in

feasible directions, to within the default value of the function tolerance,

and constraints were satisfied to within the default value of the constraint tolerance.

<stopping criteria details>

Active inequalities (to within options.TolCon = 1e-006):

lower upper ineqlin ineqnonlin

1

x =

0.55221.20330.9478

y =

10.6511

>>

---