I have observed that the function \tau_1 log\left( 1 + \frac{\mathbf {A_i} \tau_0 + \mathbf {D_i} \tau_1 }{\mathbf{B_i} \tau_0 +c \tau_1 }\right) is jointly convex w.r.t \{\tau_0,\tau_1 \}.

So, it can be transformed to a CVX acceptable form using the ‘rel_entr(x,y)’ function.

I didn’t succeed to transform this function to the appropriate form. Your suggestions/hints are highly appreciated. Please help. Thanks in advance.

Have you tried applying my previous suggestion to you at How to implement following function in CVX? ?