Konvertieren eines semidefinite Programm von CVX

Question

CVXPY ich folgende SDP konvertieren möchten - die nur die Machbarkeit der Einschränkungen überprüft - von CVX (MATLAB) zu 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 

Unten ist mein 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 

Beim Ausführen des Programms treten mehrere Fehler auf. 1. Wenn ich MBLK drucken, zeigt es

Traceback (most recent call last):

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

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

File "", line 1, in

Mblk

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

format_dict, md_dict = self.compute_format_data(result)

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

return self.shell.display_formatter.format(result)

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

data = formatter(obj)

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

printer.pretty(obj)

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

return _default_pprint(obj, self, cycle)

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

p.text(repr(obj))

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

', ', "array(")

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

separator, prefix, formatter=formatter)

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

'int' : IntegerFormat(data),

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

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

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

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

Exception: Cannot evaluate the truth value of a constraint.

Wenn ich auf diese Linie Schritt,

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] 

es

Traceback (most recent call last): File

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

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

ValueError: setting an array element with a sequence.

Wie zeigt diese Probleme zu beheben?

Answer 1

Das große Problem mit Ihrem Code ist, dass Sie NumPy-Funktionen nicht auf CVXPY-Objekten verwenden können. Sie müssen die entsprechenden CVXPY-Funktionen verwenden. Hier ist eine funktionierende Version des Codes:

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 

ich die kron Funktion entfernt, weil es hier nichts zu tun war und CVXPY unterstützt derzeit keine Kronecker-Produkte mit einer variablen linken Seite. Ich kann es hinzufügen, wenn Sie es brauchen.