Syntax of recurrence formula not clear

Question

I have this task for Analysis of Algorithms module in university

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

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 $i\colon w_i<w$ does not really make sense to me. Could someone please explain this to me?