Optimization for fat line intersecting most points Let's say I have a bunch of $(X,Y)$ points in 2D space. I want to find the line $y=mx+b$ which intersects the most points. We can add some kind of buffer (a delta) so if the line $y=mx+b$ is within delta of the point, then it also intersects the point.
I've never taken any optimization theory, but I'd assume this is a pretty simple optimization problem. I'm having some trouble formalizing the objective function to maximize/minimize, so any help with that would be awesome.
Thanks,
Michael 

Your optimization problem can be formulated as
$$\min_{m,b \in \mathbb{R}} \|Y-mX-b\|_0,$$
where $\|\cdot\|_0$ is the $\ell^0$ semi-norm defined as $\|v\|_0 = \#\{v_i \neq 0\}$ (See here). 
The only drawback is that $\|\cdot\|_0$ is not convex, thus you cannot employ the classical convex optimization tools.
