I know this optimization is not convex. But, when I just play with 1/(1+exp(-a)), it is solvable. However, when I add a linear component, it becomes unsolvable. As we all know, the linear component does not change the convexity property of the original problem. So I think there much be some way to transform the problem into a cvx-solvable one.
Take a look at the CVX manual for “log-convexity”. Your problem is not, in fact, CVX solvable. I concede that the issue is obscured by the fact that CVX accepted a non-convex result, but you got lucky there. It is non-convex and you’re not going to be able to take it further.