【python 3.7.5 求解二次规划】MATLAB函数quadprog的python 实现

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