【python 3.7.5 求解二次规划】MATLAB函数quadprog的python 实现
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matlab 使用quadprog 函数，求解线性规划，二次规划等问题。那么如何保持跟matlab 相同的参数，python使用习惯呢，下面定义一个函数，符合matlab用户的使用习惯。简单例子如下：
import numpy as np
import cvxopt
def quadprog(H, f, L=None, k=None, Aeq=None, beq=None, lb=None, ub=None):
"""
Input: Numpy arrays, the format follows MATLAB quadprog function: https://www.mathworks.com/help/optim/ug/quadprog.html
Output: Numpy array of the solution
"""
n_var = H.shape[1]
P = cvxopt.matrix(H, tc='d')
q = cvxopt.matrix(f, tc='d')
if L is not None or k is not None:
assert(k is not None and L is not None)
if lb is not None:
L = np.vstack([L, -np.eye(n_var)])
k = np.vstack([k, -lb])
if ub is not None:
L = np.vstack([L, np.eye(n_var)])
k = np.vstack([k, ub])
L = cvxopt.matrix(L, tc='d')
k = cvxopt.matrix(k, tc='d')
if Aeq is not None or beq is not None:
assert(Aeq is not None and beq is not None)
Aeq = cvxopt.matrix(Aeq, tc='d')
beq = cvxopt.matrix(beq, tc='d')
sol = cvxopt.solvers.qp(P, q, L, k, Aeq, beq)
return np.array(sol['x'])
if __name__ == '__main__':
H=np.array([[1,-1],[-1,2]])
print(H)
f=np.array([[-2],[-6]])
print(f)
L=np.array([[1,1],[-1,2],[2,1]])
print(L)
k=np.array([[2],[2],[3]])
print(k)
res=quadprog(H, f, L,k)
print(res)
运行结果：
[[ 1 -1]
[-1 2]]
[[-2]
[-6]]
[[ 1 1]
[-1 2]
[ 2 1]]
[[2]
[2]
[3]]
pcost dcost gap pres dres
0: -1.1510e+01 -8.7580e+00 3e+00 9e-01 7e-16
1: -9.1195e+00 -8.5750e+00 3e-01 1e-01 2e-16
2: -8.3243e+00 -8.2258e+00 2e-01 3e-02 6e-16
3: -8.2233e+00 -8.2223e+00 2e-03 3e-04 2e-16
4: -8.2222e+00 -8.2222e+00 2e-05 3e-06 2e-16
5: -8.2222e+00 -8.2222e+00 2e-07 3e-08 7e-17
Optimal solution found.
[[0.6666667 ]
[1.33333334]]
参考百度文库：二次规划教程