Here is the question that I meet.
$$\min_z{\sum_j{\max(0,\Vert z-f_j\Vert_2^2-m_j^2)}}$$
Intuitively speaking, I want to obtain a point $z$ that is nearest to all other points $f_j$, but, when the distance between $f_j$ and $z$ is less than $m_j$, the loss can be omitted.
I cannot solve this problem with a closed form solution, but I can get the optimal solution by enumerating all possible cases through fixing whether the point $z$ is in the circle of $f_j$ or not.
I want to know that if there are any methods that I can use to tackle this problem?