What does $\max_{i=1}^k (f_i(x) - q_i)$ mean?
Is it a sum?
This is the Chebyshev achievement function. And it's taken in "$L^{\infty}$ sense".
The optimization problem related to this is written:
$$\min_{x \in S}\max_{i=1}^k (f_i(x) - q_i) $$
Does this mean that one finds first index $i$ or $x$?