Imagine you are trying to solve an optimization problem and your goal is to pick a set of parameters, $p_1$ to $p_i$ that a given cost function $f$ is minimized based on a set of constraints.
What does it mean mathematically when two of these parameters are in conflict with each other meaning that picking any value for $p_n$ cause another parameter such as $p_m$ to be zero. in other words, they cannot coexist. This is probably the definition of "you can not have it all"!!
In other words, how to do we mathematically express and formulate conflicting optimization parameters?
This sounds like the constraint "$p_m p_n = 0$". If that's not what you mean, you may need to provide a bit more detail in your Question.