Interpreting minimum notation in a sum

Question

I've been given the equation:

$\sum_{j=1, j \neq i}^N \min_{b_j}{\{f(a_i, b_j)-f(c_i, b_j)\}} $

I'm confused about what the $\min_{b_j}$ is for; is it referring to the minimum between $f(a_i, b_j)$ and $f(c_i, b_j)$, or the minimum possible value of $b_j$ to solve what's in the braces??

Answer 1

I believe $i$ is given. So the notation stands for the minimum value of $f(a_i,b_j)-f(c_i,b_j)$ in terms of $b_j$, meaning you plug in all values of $b_j$ and look for the minimum value of $f(a_i,b_j)-f(c_i,b_j)$.