How to solve it about CVX' function?

[Michal_Adamaszek]

Here:

Can CVX handle the function log_det( I + inv(X) )

I believe t \geq \log(\det( I + {\rm inv}(X) )) is equivalent to -t \leq \log(\det( I - {\rm inv}(X+I) )) is equivalent to -t \leq \log(\det( I - U )) U \succeq {\rm inv}(X + I) is equivalent to -t \leq \log(\det( I - U )) \left[\begin{array}{cc}X+I & I\\I & U\end{array}\right] \succeq 0 The first step follows from the scalar to matrix generalization above which you can prove more rigidly. The second step follows by applying \log(\det( I - U )) \leq \log(\det( I - V )) on I \succeq U \…