For example, my objective function represents the multi-user utility sum (linear expression), but before adding it, I need to determine whether the user is within the service range. There is a convex inequality here. However, in cvx objective function, if/else is not allowed. So how do I deal with this problem. If I simply add the 01 variable to replace the if/else, then my objective function will become a non-convex function.

See

Posts containing ‘logic constraints big m’ - Operations Research Stack Exchange

and

whose logic constructs also apply to CVX (except CVX doesn’t have `implies`

).