The current proximal approximation approach does not allow you to start with no cuts.
This PR would update the proximal approximation code such that:
Allows for starting with an empty set of cuts
Makes starting with the empty set of cuts the new default
Adds two cuts per pass: the "nearest point" cut (i.e., at x = argmin [( x - \hat{x} )^2 + ( x^2 - \hat{y} )^2] and the "straightforward projection cut" (i.e., at x = \hat{x}). Before we just added the "nearest point" cut.
The current proximal approximation approach does not allow you to start with no cuts.
This PR would update the proximal approximation code such that: