the function is concave in Rx how write in cvx as it is not taking inverse and getting error as Invalid data type. Input matrix must be double or single.
where Rx,Rmse,RH are psd
and . is hadamard product.
and . is hadamard product.
Please show us your proof of concavity of the objective function.
As for Invalid data type. Input matrix must be double or single., we would need to see a reproducible example Apparently, some input data is not a single or double precision MATLAB variable (number).
as Rmse, Rx, RH are positive semi definite when logdet(X) is concave the entries of X should be positive definite, so the above function det() is positive definite, then it will become log concave.
That “proof” doesn’t convince me. Please provide a solid proof.
Perhaps you can start with a proof in the scalar case. Validity in the scalar case is necessary but not sufficient for validity in the matrix case.
You can see what to do in the scalar case at Can CVX solve this kind of function {x-log(1+0.01*x/(x+1))} - #15 by Mark_L_Stone
if this actually is concave for the matrix case, maybe (maybe!!) there is some way to do it using one or more of determinantal identities, Schur complement, or quantum functions in
or
https://qetlab.com/ .
Could you please tell me how can I write inverse function in cvx.
You can’t in general. There are some special functions such as inv_pos, matrix_frac, det_inv, prod_inv, and trace_inv, which can be used in accordance with their help entries.
could you please look into this , log_det: log of determinant of a positive definite matrix, log det(X). When
used inside a cvx specification, log_det constrains its argument to be symmetric (if real) or Hermitian (if complex) and positive definite. With numerical
argument, log_det returns -Inf if these constraints are not met. Concave.
Here is the more detailed information from help.
help log_det
log_det Logarithm of the determinant of an SDP matrix.
For a square matrix X, log_det(X) returns
LOG(DET(X))
if X is symmetric (real) or Hermitian (complex) and positive semidefinite,
and -Inf otherwise.When used in a CVX model, log_det(X) causes CVX's successive approximation method to be invoked, producing results exact to within the tolerance of the solver. Therefore, whenever possible, the use of DET_ROOTN(X) is to be preferred, because the latter choice can be represented exactly in an SDP. For example, the objective MAXIMIZE(log_det(X)) can be (and should be) replaced with MAXIMIZE(DET_ROOTN(X)) in fact, log_det(X) is implemented simply as N*LOG(DET_ROOTN(X)). Disciplined convex programming information: log_det is concave and nonmonotonic; therefore, when used in CVX specifications, its argument must be affine.
The argument of log_det must be affine, which yours isn’t.
As my function log_det arguments is not affine because of inverse. so we cannot do in cvx right?
If the objective function is not concave, you can’t maximize it in CVX. If it is, you might be able to, but not necessarily. Please carefully read the link in my first post.