MMA二次规划示例

青青子衿

1. z = Symbol["x" <> ToString[#]] & /@ Range[5];
2. NMinimize[{
3.   (z - {-2, 3, -7, 4, -10}) . (z - {-2, 3, -7, 4, -10}),
4.   {84, 59, 92, 31, -93} . z <= -89 &&
5.    {70, 87, 36, 52, 49} . z <= -182}, z]

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1. z = Symbol["x" <> ToString[#]] & /@ Range[5];
2. u = {-2, 3, -7, 4, -10};
3. A = {{84, 59, 92, 31, -93}, {70, 87, 36, 52, 49}};
4. b = {-89, -182};
5. A . z \[VectorLessEqual] b
6. Qmin = QuadraticOptimization[(z - u) . (z - u)(*目标函数*),
7.   A . z \[VectorLessEqual] b(*约束条件*),
8.   z (*变量*)]
9. (z - u) . (z - u) /. Qmin

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1. %% 【Matlab】%%
2. alpha_1=[84; 59; 92; 31; -93];
3. alpha_2=[70; 87; 36; 52; 49];
4. u=[-2; 3; -7; 4; -10];
5. b_1 = -89;
6. b_2 = -182;
7. % 定义优化问题相关量
8. H = eye(m); % Hessian matrix
9. f = -u; % linear term
10. c = u'*u/2; % constant term
11. % 约束条件
12. A = [alpha_1'; alpha_2'];
13. b = [b_1, b_2];
14. % 求解优化问题
15. [z, fval] = quadprog(H, f, A, b, [], [], [], [], []);
16. % 返回值
17. z
18. Fval=2*(fval+c)

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