Notation for the element with the maximum value

Question

I have a set of elements $A$ and a function which assigns a value $d_{a}$ to each element $a\in A$.

I am looking for a notation for the element $a$ with the lowest value $d_{a}$.

What I have found so far is the argmax function, but I am not sure if I am using it correctly or if I even need to use it:

$a_{max} = \arg\max_{a\in A}(d_{a})$

Answer 1

Please notice your title contradicts the body of your question: you state in the title you need notation for the argument value giving the maximum value of the function, while according to the body, you need notation for the argument value giving the minimum value of the function.

Assuming the body is correct, then apart from that you obviously need $\arg\min$, your usage is absolutely correct.

For better typesetting, you can use the \limits $\LaTeX$ operator like that: $$\arg\min\limits_{a\in A}\left(d_a\right);$$ the $\LaTeX$ source for the above is as follows: \arg\min\limits_{a\in A}\left(d_a\right);.

Answer 2

I am looking for a notation for the element aa with the lowest value dada.

Therefore the notation you're looking for is rather $\arg \min_{a \in A} d_a$. This notation literally means the element $a$ of $A$ such that $d_a$ is minimum.