Given some fixed $n \in \mathbb{N}$, I want to minimize the following function of $i$:
$$L(i, n) = \Bigl\lceil \frac{n}{i} \Bigr\rceil + i$$
within limits $1 \leq i \leq \bigl\lceil \frac{n}{2} \bigr\rceil,\; i \in \mathbb{N}$
Can somebody help me find some sort of a closed form expression for the $i$ that minimizes $L(i, n)$ given a particular $n$?