求解二次规划问题的最优解miny=11787-27.7x1-77.5x5-172.8x3^2+0.1x5^2+3.7x2x4+0.1x1x5-3.1x4x5+482.4x3x4,matlab代码

可以使用MATLAB中的quadprog函数求解二次规划问题的最优解。具体步骤如下：

1. 定义二次规划问题的目标函数、约束条件和变量范围。

H = [345.6, 0, 0, -345.6, 482.4; 
     0, 0, 3.7, 0, 0; 
     0, 3.7, -345.6, 0, 0; 
     -345.6, 0, 0, 691.2, -3.1; 
     482.4, 0, 0, -3.1, 0.2];
f = [-27.7; 0; 0; 0; 0];
A = [0, 0, 1, 0, 0; 
     1, 0, 0, 0, 0; 
     0, 0, 0, 0, 1];
b = [0; -11787; 0];
lb = [-inf; -inf; -inf; -inf; -inf];
ub = [inf; inf; inf; inf; inf];

其中，H是二次项系数矩阵，f是一次项系数矩阵，A和b是不等式约束条件，lb和ub是变量范围。

2. 调用quadprog函数求解最优解。

[x, y, exitflag] = quadprog(H, f, A, b, [], [], lb, ub);

其中，x是最优解向量，y是拉格朗日乘子向量，exitflag是求解状态。

3. 输出最优解。

miny = f' * x;
fprintf('The minimum value of the objective function is %f.\n', miny);
fprintf('The optimal solution is x1 = %f, x2 = %f, x3 = %f, x4 = %f, x5 = %f.\n', x(1), x(2), x(3), x(4), x(5));

完整的MATLAB代码如下：

H = [345.6, 0, 0, -345.6, 482.4; 
     0, 0, 3.7, 0, 0; 
     0, 3.7, -345.6, 0, 0; 
     -345.6, 0, 0, 691.2, -3.1; 
     482.4, 0, 0, -3.1, 0.2];
f = [-27.7; 0; 0; 0; 0];
A = [0, 0, 1, 0, 0; 
     1, 0, 0, 0, 0; 
     0, 0, 0, 0, 1];
b = [0; -11787; 0];
lb = [-inf; -inf; -inf; -inf; -inf];
ub = [inf; inf; inf; inf; inf];
[x, y, exitflag] = quadprog(H, f, A, b, [], [], lb, ub);
miny = f' * x;
fprintf('The minimum value of the objective function is %f.\n', miny);
fprintf('The optimal solution is x1 = %f, x2 = %f, x3 = %f, x4 = %f, x5 = %f.\n', x(1), x(2), x(3), x(4), x(5));