I want to solve an optimization that minimize log_det( I + inv(X) ) under the semidefinite constraint and some linear constraints to X. For the background of this problem, see this reference.
As mentioned in this reference, though log_det( I + inv(X) ) is a convex function of X, numerically solving the problem is not easy.
I tried to express the function in CVX as
log_det( I + inv(X) ) and
log_det( X + I ) - log_det( X ). However, CVX cannot accept these expressions.
I want to know whether CVX is able to handle the function. If not, is there any other softwares that can handle the function?