How is this not just a linear least squares estimation of the two unknown parameters? There is nothing binary about this, except that you have two unknowns. That is a misuse of the word, and will just confuse people.
As far as the quadratic optimization goes, again, you are trying define the problem in terms of flowery words, when a simple solution exists.
While you can use polyfit but for the constraints, those constraints make it a problem for lsqlin, which can trivially solve your problem. This is a simple linear least squares estimation problem, subject to linear inequality constaints.
