I have a circle with radius $R$ and $N$ points on a 2D plane with known locations $(x_i,y_i), i=1,2,..N$. I want to place the circle such that it maximizes the number of covered points.
Let $d_i=(x_i-x)^2+(y_i-y)^2$ be the square of the distance between the point $i$ and the potential center of the circle $(x,y)$. To ensure point $i$ is within the circle, $d_i$ must satisfy $d_i\leq R^2$. This condition can be formulated by introducing a binary variable $u_i$ such that $u_i=1$ if point $i$ is inside the circle and $u_i=0$ otherwise. Then, we have
My question, does the constraint above model my problem correctly?.