The optimization problem I need to solve is provided in the following link:

https://math.stackexchange.com/q/4637659/1149147

I tried to solve this for p = 2 using cvx MATLAB with the code below:

cvx_begin sdp quiet

variable A0(3,3) symmetric

variable b0(3)

variable tau1 nonnegative

variable tau2 nonnegative

minimize(log(det_inv(A0)))

subject to

[A0 b0 0;b0’ -1 b0’;0 b0 -A0] - tau1*[A1 b1 0; b1’ c1 0;0 0 0] <= 0;

[A0 b0 0;b0’ -1 b0’;0 b0 -A0] - tau2*[A2 b2 0; b2’ c2 0;0 0 0] <= 0;

cvx_end

But it is showing the following error:

CVX Warning:

Models involving “log” or other functions in the log, exp, and entropy

family are solved using an experimental successive approximation method.

This method is slower and less reliable than the method CVX employs for

other models. Please see the section of the user’s guide entitled

The successive approximation method

for more details about the approach, and for instructions on how to

suppress this warning message in the future.

Error

Error using cvx/log

Disciplined convex programming error

Illegal operation: log( { convex} ).