将半定程序从CVX转换为CVXPY [英] Convert a semidefinite program from CVX to CVXPY

问题描述

我想将以下 SDP(它只是验证约束的可行性)从 CVX (MATLAB) 转换为 CVXPY (Python):

I want to convert the following SDP — which just verifies the feasibility of the constraints — from CVX (MATLAB) to CVXPY (Python):

Ah = [1.0058, -0.0058; 1, 0];
Bh = [-1; 0];
Ch = [1.0058, -0.0058; -0.9829, 0.0056];
Dh = [-1; 1];

M = [0, 1;1, 0];
ni = size(M,1)/2;
n = size(Ah,1);
rho = 0.5;

cvx_begin sdp quiet
    variable P(n,n) semidefinite
    variable lambda(ni) nonnegative
    Mblk = M*kron(diag(lambda),eye(2));
    lambda(ni) == 1  % break homogeneity (many ways to do this...)
    [Ah Bh]'*P*[Ah Bh] - rho^2*blkdiag(P,0) + [Ch Dh]'*Mblk*[Ch Dh] <= 0
cvx_end


switch cvx_status
    case 'Solved'
        feas = 1;
    otherwise
        feas = 0;
end

下面是我的Python代码，

Below is my Python code,

import cvxpy as cvx
import numpy as np
import scipy as sp


Ah = np.array([[1.0058, -0.0058], [1, 0]])
Bh = np.array([[-1], [0]])
Ch = np.array([[1.0058, -0.0058], [-0.9829, 0.0056]])
Dh = np.array([[-1], [1]])

M = np.array([[0, 1], [1, 0]])
ni, n = M.shape[0] / 2, Ah.shape[0]
rho = 0.5

P = cvx.Semidef(n)
lamda = cvx.Variable()

Mblk = np.dot(M, np.kron(cvx.diag(lamda), np.eye(2)))
ABh = np.concatenate((Ah, Bh), axis=1)
CDh = np.concatenate((Ch, Dh), axis=1)
constraints = [lamda[-1] == 1,
               np.dot(ABh.T, np.dot(P, ABh)) - rho**2*np.linalg.block_diag(P, 0) +
               np.dot(CDh.T, np.dot(Mblk, CDh)) << 0]

prob = cvx.Problem(cvx.Minimize(1), constraints)
feas = prob.status is cvx.OPTIMAL

运行程序时出现几个错误.1.当我打印Mblk时，它会显示

There are several errors when I run the program. 1. When I print Mblk, it shows

回溯(最近通话最近一次):

Traceback (most recent call last):

文件"/usr/lib/python2.7/dist-packages/IPython/core/interactiveshell.py"，第2820行，在run_code中

File "/usr/lib/python2.7/dist-packages/IPython/core/interactiveshell.py", line 2820, in run_code

Out [1]:self.user_global_ns，self.user_ns中的exec code_obj

Out[1]: exec code_obj in self.user_global_ns, self.user_ns

文件"，位于

兆位

文件"/usr/lib/python2.7/dist-packages/IPython/core/displayhook.py"，第247行，在致电

File "/usr/lib/python2.7/dist-packages/IPython/core/displayhook.py", line 247, in call

format_dict，md_dict = self.compute_format_data(结果)

format_dict, md_dict = self.compute_format_data(result)

文件"/usr/lib/python2.7/dist-packages/IPython/core/displayhook.py"，第157行，在compute_format_data中

File "/usr/lib/python2.7/dist-packages/IPython/core/displayhook.py", line 157, in compute_format_data

返回self.shell.display_formatter.format(结果)

return self.shell.display_formatter.format(result)

文件"/usr/lib/python2.7/dist-packages/IPython/core/formatters.py"，第152行，格式为

File "/usr/lib/python2.7/dist-packages/IPython/core/formatters.py", line 152, in format

数据=格式化程序(obj)

data = formatter(obj)

文件/usr/lib/python2.7/dist-packages/IPython/core/formatters.py"，第481行，在致电

File "/usr/lib/python2.7/dist-packages/IPython/core/formatters.py", line 481, in call

printer.pretty(obj)

printer.pretty(obj)

文件"/usr/lib/python2.7/dist-packages/IPython/lib/pretty.py"，行362，漂亮

File "/usr/lib/python2.7/dist-packages/IPython/lib/pretty.py", line 362, in pretty

返回_default_pprint(obj，self，cycle)

return _default_pprint(obj, self, cycle)

文件"/usr/lib/python2.7/dist-packages/IPython/lib/pretty.py"，行482，在_default_pprint

File "/usr/lib/python2.7/dist-packages/IPython/lib/pretty.py", line 482, in _default_pprint

p.text(repr(obj))

p.text(repr(obj))

文件"/usr/lib/python2.7/dist-packages/numpy/core/numeric.py"，行1553，在array_repr中

File "/usr/lib/python2.7/dist-packages/numpy/core/numeric.py", line 1553, in array_repr

'，'，"array(")

', ', "array(")

文件"/usr/lib/python2.7/dist-packages/numpy/core/arrayprint.py"，行454，在array2string中

File "/usr/lib/python2.7/dist-packages/numpy/core/arrayprint.py", line 454, in array2string

分隔符，前缀，formatter = formatter)

separator, prefix, formatter=formatter)

文件"/usr/lib/python2.7/dist-packages/numpy/core/arrayprint.py"，行256，以_array2string

File "/usr/lib/python2.7/dist-packages/numpy/core/arrayprint.py", line 256, in _array2string

'int':IntegerFormat(数据)，

'int' : IntegerFormat(data),

文件"/usr/lib/python2.7/dist-packages/numpy/core/arrayprint.py"，行641，在 init

File "/usr/lib/python2.7/dist-packages/numpy/core/arrayprint.py", line 641, in init

max_str_len = max(len(str(max(maximum.reduce(data)))，

max_str_len = max(len(str(maximum.reduce(data))),

文件"/usr/local/lib/python2.7/dist-packages/cvxpy/constraints/leq_constraint.py"，第67行，非零

File "/usr/local/lib/python2.7/dist-packages/cvxpy/constraints/leq_constraint.py", line 67, in nonzero

引发异常(无法评估约束的真值.")

Raise Exception("Cannot evaluate the truth value of a constraint.")

异常:无法评估约束的真值.

Exception: Cannot evaluate the truth value of a constraint.

当我走到这一行时，

  constraints = [lamda[-1] == 1,
                   np.dot(ABh.T, np.dot(P, ABh)) - rho**2*np.linalg.block_diag(P, 0) +
                   np.dot(CDh.T, np.dot(Mblk, CDh)) << 0]

它显示

回溯(最近通话最近一次):文件

Traceback (most recent call last): File

".../sdp.py"，第22行，位于

".../sdp.py", line 22, in

np.dot(ABh.T, np.dot(P, ABh)) - rho**2*np.linalg.block_diag(P, 0) + 

ValueError:设置具有序列的数组元素.

ValueError: setting an array element with a sequence.

如何解决这些问题?

推荐答案

您的代码的最大问题是您不能在CVXPY对象上使用NumPy函数.您需要使用等效的CVXPY函数.这是您的代码的有效版本:

The big issue with your code is that you can't use NumPy functions on CVXPY objects. You need to use the equivalent CVXPY functions. Here's a working version of your code:

import cvxpy as cvx
import numpy as np
import scipy as sp


Ah = np.array([[1.0058, -0.0058], [1, 0]])
Bh = np.array([[-1], [0]])
Ch = np.array([[1.0058, -0.0058], [-0.9829, 0.0056]])
Dh = np.array([[-1], [1]])

M = np.array([[0, 1], [1, 0]])
ni, n = M.shape[0] / 2, Ah.shape[0]
rho = 0.5

P = cvx.Semidef(n)
lamda = cvx.Variable()

Mblk = M*lamda*np.eye(2)
ABh = cvx.hstack(Ah, Bh)
CDh = cvx.hstack(Ch, Dh)
zeros = np.zeros((n,1))
constraints = [lamda[-1] == 1,
               ABh.T*P*ABh - rho**2*cvx.bmat([[P,zeros],[zeros.T, 0]]) +
               CDh.T*Mblk*CDh << 0]

prob = cvx.Problem(cvx.Minimize(1), constraints)
prob.solve()
feas = prob.status is cvx.OPTIMAL

我删除了kron函数，因为它在这里没有做任何事情，并且CVXPY当前不支持左侧可变的Kronecker产品.我可以根据需要添加它.

I removed the kron function because it wasn't doing anything here and CVXPY doesn't currently support Kronecker products with a variable left-hand side. I can add it if you need it.

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