How to solve min-max problem in CVX?

A similar question has been asked here

I am wondering, how could I define the auxiliary variable to solve this min-max problem in CVX? Is there any particular rule to be followed in CVX?

The chance of getting a useful answer will be increased if you completely describe a sample problem of interest.

You may not even need an auxiliary variable.
max of convex expression arguments is a convex expression which can be minimized. For instance, this made-up (useless) problem is valid CVX code:

variable x(4)

Thank you. This helps. I will post the MWE once I complete the code.