Hi,
The problem I am trying to solve in cvx is:
minimize \left(\frac{1-\tau_j}{\tau_j}\right)\sigma + \left[\frac{1}{\tau_j}\prod\limits_{k\neq j}^{N}\left(1+\frac{R_k}{R_j}\frac{\tau_j}{1-\tau_j}\right)-\frac{1}{\tau_j}\right]\frac{L}{R_i}
subject to 0 \leq \tau_j \leq 1
where \tau_j is the variable of optimization.
\sigma, L and R_i, \forall i are constants.
I am facing two problems with the above formulation:
(a) CVX does not accept product of convex terms i.e. I am unable to write the expression i.e. \prod\limits_{k\neq j}^{N}\left(1+\frac{R_k}{R_j}\frac{\tau_j}{1-\tau_j}\right) in cvx.
(b) Although the objective function is convex, the term in expressions i.e. \left[\frac{1}{\tau_j}\prod\limits_{k\neq j}^{N}\left(1+\frac{R_k}{R_j}\frac{\tau_j}{1-\tau_j}\right)-\frac{1}{\tau_j}\right]\frac{L}{R} consists of \left(-\frac{1}{\tau_j}\right) that is treated as concave and hence cvx gives me error Illegal operation: {convex} + {concave}.
This seems to be a standard convex optimization problem. How can it be formulated using cvx?