Section 7.1.1: Covariance estimation for Gaussian variables
randn('state',0);
n = 10;
N = 1000;
tmp = randn(n);
L = tmp*tmp';
tmp = randn(n);
U = L + tmp*tmp';
R = (L+U)/2;
y_sample = sqrtm(R)*randn(n,N);
Y = cov(y_sample');
Ui = inv(U); Ui = 0.5*(Ui+Ui');
Li = inv(L); Li = 0.5*(Li+Li');
cvx_begin sdp
variable S(n,n) symmetric
maximize( log_det(S) - trace(S*Y) );
S >= Ui;
S <= Li;
cvx_end
R_hat = inv(S);
Successive approximation method to be employed.
SDPT3 will be called several times to refine the solution.
Original size: 356 variables, 122 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
Approximation size: 365 variables, 127 equality constraints
-----------------------------------------------------------------
Target Conic Solver
Precision Error Status
---------------------------
1.221e-04 7.339e-01 Solved
1.221e-04 1.481e-04 Solved
1.221e-04 0.000e+00 Solved
1.490e-08 0.000e+00 Solved
-----------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -30.6698