# The following optimization function is interpreted correctly?

I want to confirm if I interpreted following optimization function correctly?

Let's say we have a set of nodes (say users connected to a Base Station in cellular network), denoted as, $$U={u_1,u_2,...,u_M}$$ and let $$Throughput(u_m), \forall u_m \in U$$ be a function (say throughput calculating function) defined on each element in $U$.

I define an optimization problem as, "find a user in $U$ such that it has the minimum throughput."

For above optimization problem, I define following function,$$i\gets \underset{m\ :\ u_m\in \ U}{argmin} \ Throughput(u_m)$$

I want to confirm if I have interpreted the function correctly?

Thanks!

The sentence you give and the notation (defining a variable $i$) give the same meaning; they both give you a user. However, an optimization problem should be defined in terms of numbers... not "users". So for an optimization problem, you would want to probably optimize $Throughput(i)$, that is $$\min_{u_m \in U} Throughput(u_m)$$