python 二次规划（argmax）问题

求解argmax时用到二次规划，matlab中 quadprog使用很简单，但是在python中这一类资料却很少，网上给出的大部分答案都是，但是对各个变量的说明几乎没有，我带入自己的变量时总是报错

def quadprog_solve_qp(P, q, G=None, h=None, A=None, b=None):
    qp_G = .5 * (P + P.T)   # make sure P is symmetric
    qp_a = -q
    if A is not None:
        qp_C = -numpy.vstack([A, G]).T
        qp_b = -numpy.hstack([b, h])
        meq = A.shape[0]
    else:  # no equality constraint
        qp_C = -G.T
        qp_b = -h
        meq = 0
    return quadprog.solve_qp(qp_G, qp_a, qp_C, qp_b, meq)[0] 

最后使用了另一个module qpsolvers解决了二次规划问题

1. 待解决的二次规划如下：

from qpsolvers import solve_qp
from cvxopt import matrix
def reg_LASSO(phi, output, lam, dim_the=6):
    h = phi.dot(phi.T) # φ(x) function
    P = matrix(np.vstack((np.hstack((h, -h)), np.hstack((-h, h))))) # coefficient matrix of x^2 
    q =  matrix(np.squeeze(lam*np.ones(shape=(dim_the*2,1))-np.concatenate((phi.dot(output),-phi.dot(output)), axis=0)) )# coefficient matrix of x^1

    G = matrix(-np.eye((dim_the*2))) # coefficient matrix(left) of  constrained condition
    h = matrix(np.zeros(shape=(dim_the*2,1))) # coefficient matrix(right) of  constrained condition
    the = solvers.qp(P, q, G, h)['x']# output of this function is a dict
    the = the[0:dim_the,:]-the[dim_the:,:]
    return the

numpy 点乘连乘的简单写法

a.dot(b).dot(c) # a,b and c are numpy array

2. 一次型

import scipy
def reg_RR(phi, output, lam=1, dim_the=6):
    [d,n] = phi.shape
    f = matrix(np.vstack((np.zeros((d,1)),np.zeros((n,1)))))
    A = matrix(np.vstack((np.hstack((-phi.T, -np.eye(n))),np.hstack((phi.T,-np.eye(n))))))
    b = np.vstack((-output,output))
    the = scipy.optimize.linprog(f,A,b)['x']
    the = the[0:d,np.newaxis]
    return the

3. numpy array 的逆矩阵不能用A.I，要用np.linalg.inv(A)