Please provide a detailed description, or at least an example, of the mathematical problem (functions) you are trying to model. What is the optimization problem you want to model and solve in CVX? The more detailed and clear the information you provide, the better the chance you will get useful help

Even if a were 1, so that both “branches” were the same, this is non-convex. See Cvx expression divide problem . No matter how many times you ask or how badly you want it to be convex, it is not.

No. The list of accepted functions in the documentation is complete. If your model cannot be built according to the DCP ruleset using those functions only, CVX cannot solve it.