Infeasibility of the model suggests that the model formulation and/or it’s input data may not be adequate, or your real world problem has no solution.
If the problem you enter in an optimization modeling tool is infeasible, it may also be that any approximation made between that problem and the problem you really want to solve is inadequate.
If the problem involving the sum of logs in the objective function is a convex optimization problem, it might be enterable in CVX.
Before proceeding with CVX, carefully read