Syntax of recurrence formula not clear I have this task for Analysis of Algorithms module in university 

$$
\begin{align*}
W, V &amp;= \{v_1, v_2, v_n\}, S = \{s_1, s_2, s_n\}\\
G(W) &amp;= \max~_{i:w_i\leq w} ~\{G(W-s_i) + v_i\}, G(0)=0\\
\end{align*}
$$

I am not sure what does the marked text mean in this recurrence formula. Because I think $W$ is a variable not an array so $i\colon w_i&lt;w$ does not really make sense to me. Could someone please explain this to me?
The notation is a crossover between

$\qquad\displaystyle \max_{i}$

and

$\qquad\displaystyle \max \{ \dots \mid i \}$.

It means the same as

$\qquad\displaystyle \max \{ G(W - s_i) + v_i \mid 0 \leq i \leq n, w_i \leq W \}$,

guessing about the domain of $i$.