数学建模 非线性规划

一个很好的例子，列出优化模型和里面的约束条件

求解：

示例

求解结果

(x取（1,1）时获得最小值10)

>> main

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 optimality tolerance,
and constraints are satisfied to within the default value of the constraint tolerance.

<stopping criteria details>


x =

    1.0000
    1.0000


y =

   10.0000

% 主函数
options=optimset;
[x,y]=fmincon('func1',rand(2,1),[],[],[],[],zeros(2,1),[],'func2',options)

%目标函数
function f=func1(x);
f=x(1).^2+x(2).^2+8;

%非线性向量函数（非线性约束）
function [g,h]=func2(x);
g=-x(1).^2+x(2);
h=-x(1)-x(2).^2+2;

求解结果

>> main

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 optimality tolerance,
and constraints are satisfied to within the default value of the constraint tolerance.

<stopping criteria details>


x =

   86.1884
  104.2878
  126.1883
  152.6878


y =

  -43.0860

代码

% 主函数
options=optimset;
a=[1.1 1 0 0;1.21 1.1 1 0;1.331 1.21 1.1  1];
b=[440;484;532.4];
ub=[400;inf;inf;inf];
[x,y]=fmincon('func1',rand(4,1),a,b,[],[],zeros(4,1),ub,[],options)

function f=func1(x);
f=-(sqrt(x(1))+sqrt(x(2))+sqrt(x(3))+sqrt(x(4)));

还可以把约束条件都写到一个函数里，结果一样

% 主函数
[x,y]=fmincon('func1',rand(4,1),[],[],[],[],zeros(4,1),[],'func2',optimset)

%非线性向量函数（非线性约束）
function [g,ceq]=func2(x);
g(1)=x(1)-400;
g(2)=1.1*x(1)+x(2)-440;
g(3)=1.21*x(1)+1.1*x(2)+x(3)-484;
g(4)=1.331*x(1)+1.21*x(2)+1.1*x(3)+x(4)-532.4;
ceq=0;

function f=func1(x);
f=-(sqrt(x(1))+sqrt(x(2))+sqrt(x(3))+sqrt(x(4)));

来源：https://blog.csdn.net/qq_36607894/article/details/100106637