Python凸优化工具包——cvxopt

二次规划

二次规划标准型

 

例如

 

其中

\[\begin{array}{*{20}{l}}
{P = \left[ {\begin{array}{*{20}{c}}
{4,}&1\\
{1,}&2
\end{array}} \right]}&{q = \left[ {\begin{array}{*{20}{c}}
1\\
1
\end{array}} \right]}\\
\begin{array}{l}
G = \left[ {\begin{array}{*{20}{c}}
{ - 1,}&0\\
{0,}&{ - 1}
\end{array}} \right]\\
A = \left[ {\begin{array}{*{20}{c}}
{1,}&1
\end{array}} \right]
\end{array}&\begin{array}{l}
h = \left[ {\begin{array}{*{20}{c}}
0\\
0
\end{array}} \right]\\
b = 1
\end{array}
\end{array}\]

代码如下：

from cvxopt import matrix, solvers
P = 2*matrix([ [2, .5], [.5, 1] ])
q = matrix([1.0, 1.0])
G = matrix([[-1.0,0.0],[0.0,-1.0]])
h = matrix([0.0,0.0])
A = matrix([1.0, 1.0], (1,2))
b = matrix(1.0)
sol=solvers.qp(Q, p, G, h, A, b)
print(sol['x'])

 

 

 

from cvxopt import matrix
P = matrix([[1.0,0.0],[0.0,0.0]])
q = matrix([3.0,4.0])
G = matrix([[-1.0,0.0,-1.0,2.0,3.0],[0.0,-1.0,-3.0,5.0,4.0]])
h = matrix([0.0,0.0,-15.0,100.0,80.0])

　　

注：

matrix元素的类型必须是double类型，可以通过如下语句设置。

import numpy as np
from cvxopt import matrix
P = matrix(np.diag([1,0]), tc=’d’)
q = matrix(np.array([3,4]), tc=’d’)
G = matrix(np.array([[-1,0],[0,-1],[-1,-3],[2,5],[3,4]]), tc=’d’)
h = matrix(np.array([0,0,-15,100,80]), tc=’d’)

　

 

参考链接：

https://cvxopt.org/examples/index.html