CVXOPT模块怎么在Python中安装与使用

CVXOPT模块怎么在Python中安装与使用？很多新手对此不是很清楚，为了帮助大家解决这个难题，下面小编将为大家详细讲解，有这方面需求的人可以来学习下，希望你能有所收获。

CVXOPT的官方说明文档网址为：http://cvxopt.org/index.html， 现最新版本为1.1.9,由Martin Andersen, Joachim Dahl 和Lieven Vandenberghe共同开发完成，能够解决线性规划和二次型规划问题，其应用场景如SVM中的Hard Margin SVM.

CVXOPT使用举例如下：

线性规划问题

例1:

Python程序代码：

importnumpyasnp
fromcvxoptimportmatrix,solvers
A=matrix([[-1.0,-1.0,0.0,1.0],[1.0,-1.0,-1.0,-2.0]])
b=matrix([1.0,-2.0,0.0,4.0])
c=matrix([2.0,1.0])
sol=solvers.lp(c,A,b)
print(sol['x'])
print(np.dot(sol['x'].T,c))
print(sol['primalobjective'])

输出结果：

pcostdcostgappresdresk/t
0:2.6471e+00-7.0588e-012e+018e-012e+001e+00
1:3.0726e+002.8437e+001e+001e-012e-013e-01
2:2.4891e+002.4808e+001e-011e-022e-025e-02
3:2.4999e+002.4998e+001e-031e-042e-045e-04
4:2.5000e+002.5000e+001e-051e-062e-065e-06
5:2.5000e+002.5000e+001e-071e-082e-085e-08
Optimalsolutionfound.
{'primalobjective':2.4999999895543072,'s':<4x1matrix,tc='d'>,'dualinfeasibility':2.257878974569382e-08,'primalslack':2.0388399547464153e-08,'dualobjective':2.4999999817312535,'residualasdualinfeasibilitycertificate':None,'dualslack':3.529915972607509e-09,'x':<2x1matrix,tc='d'>,'iterations':5,'gap':1.3974945737723005e-07,'residualasprimalinfeasibilitycertificate':None,'z':<4x1matrix,tc='d'>,'y':<0x1matrix,tc='d'>,'status':'optimal','primalinfeasibility':1.1368786228004961e-08,'relativegap':5.5899783359379607e-08}
[5.00e-01]
[1.50e+00]

[[2.49999999]]

例2

Python程序代码

importnumpyasnp
fromcvxoptimportmatrix,solvers
A=matrix([[1.0,0.0,-1.0],[0.0,1.0,-1.0]])
b=matrix([2.0,2.0,-2.0])
c=matrix([1.0,2.0])
d=matrix([-1.0,-2.0])
sol1=solvers.lp(c,A,b)
min=np.dot(sol1['x'].T,c)
sol2=solvers.lp(d,A,b)
max=-np.dot(sol2['x'].T,d)
print('min=%s,max=%s'%(min[0][0],max[0][0]))

输出结果：

pcostdcostgappresdresk/t
0:4.0000e+00-0.0000e+004e+000e+000e+001e+00
1:2.7942e+001.9800e+008e-019e-177e-162e-01
2:2.0095e+001.9875e+002e-024e-162e-167e-03
3:2.0001e+001.9999e+002e-042e-166e-167e-05
4:2.0000e+002.0000e+002e-066e-175e-167e-07
5:2.0000e+002.0000e+002e-083e-167e-167e-09
Optimalsolutionfound.
pcostdcostgappresdresk/t
0:-4.0000e+00-8.0000e+004e+000e+001e-161e+00
1:-5.2058e+00-6.0200e+008e-011e-167e-162e-01
2:-5.9905e+00-6.0125e+002e-021e-160e+007e-03
3:-5.9999e+00-6.0001e+002e-041e-162e-167e-05
4:-6.0000e+00-6.0000e+002e-061e-162e-167e-07
Optimalsolutionfound.
min=2.00000000952,max=5.99999904803

二次型规划问题

其中P,q,G,h,A,b为输入矩阵，该问题求解采用QP算法。例1：

Python程序代码：

fromcvxoptimportmatrix,solvers
Q=2*matrix([[2,.5],[.5,1]])
p=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'])
print(sol['primalobjective'])

输出结果：

pcostdcostgappresdres
0:1.8889e+007.7778e-011e+002e-162e+00
1:1.8769e+001.8320e+004e-020e+006e-02
2:1.8750e+001.8739e+001e-031e-165e-04
3:1.8750e+001.8750e+001e-056e-175e-06
4:1.8750e+001.8750e+001e-072e-165e-08
Optimalsolutionfound.
[2.50e-01]
[7.50e-01]

例2：

Python程序代码：

fromcvxoptimportmatrix,solvers
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])
sol=solvers.qp(P,q,G,h)
print(sol['x'])
print(sol['primalobjective'])

输出结果

pcostdcostgappresdres
0:1.0780e+02-7.6366e+029e+020e+004e+01
1:9.3245e+019.7637e+008e+016e-173e+00
2:6.7311e+013.2553e+013e+016e-171e+00
3:2.6071e+011.5068e+011e+012e-177e-01
4:3.7092e+012.3152e+011e+015e-184e-01
5:2.5352e+011.8652e+017e+007e-173e-16
6:2.0062e+011.9974e+019e-022e-163e-16
7:2.0001e+012.0000e+019e-048e-175e-16
8:2.0000e+012.0000e+019e-061e-162e-16
Optimalsolutionfound.
[7.13e-07]
[5.00e+00]

20.00000617311241

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