Syntax of recurrence formula not clear
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 $i$.