I am trying to find all indices of a vector, $x=(x_1,\ldots,x_n)$, that are above a given value, $a$. I write \begin{align*} I^* = \operatorname*{argmax}_{I\subseteq\{1,\ldots,n\}}\sum_{n\in I}(x_n-a) \end{align*} Does this give me the right answer?
What's confusing to me is that $\operatorname{argmax}_xf(x) = \operatorname{argmax}_x(f(x)+c)$ for any $c$, so $I^*$ does not depend on $a$??