matlab求解下面问题max z=0.201w^4xy^2/10^7 s.t. 675-w^2x>=0 0.419-w^2*y^2/10^7>=0 0<=w<=36,0<=x<=5,0<=y<=125不要用函数定义,不允许使用函数句柄的非标量数组
时间: 2024-09-29 14:13:35 浏览: 50
在MATLAB中,你可以使用`fmincon`函数来解决这类线性规划或带有约束的最优化问题。给定的目标函数和约束条件可以表示成以下形式:
目标函数(最大化):
```matlab
z = 0.201 * w^4 * x * y^2 / 1e7;
```
约束条件:
1. w、x和y的范围限制:
```matlab
lb = [0; 0; 0]; % 下界
ub = [36; 5; 125]; % 上界
```
2. 线性不等式约束:
- 对于第一个约束:675 - w^2*x >= 0
- 对于第二个约束:0.419 - w^2*y^2 / 1e7 >= 0
可以先转换为标准形式:
```matlab
Aeq = [];
beq = zeros(0,1);
Ain = [-w.^2; zeros(size(w))]; % 矩阵Ain的负w^2部分
bin = [675; 0.419]; % 向量bin的常数项
```
现在,你可以将这些信息组合起来并调用`fmincon`函数:
```matlab
options = optimoptions('fmincon','Display','iter'); % 显示迭代信息
[x_opt, fval] = fmincon(@(w,x,y) -z, [w; x; y], [], [], [], lb, ub, Ain, beq, options);
```
这里我们选择最小化 `-z` 来找到最大值,因为`fmincon`默认是寻找最小值。
最后,变量`x_opt`, `y_opt`和`z`分别代表了最优解的x、y和目标函数的最大值。注意,在实际运行之前,你需要确保所有的变量都是向量格式,即使只有一个元素。
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