Suppose I have a linear program (LP) that has many optimal solutions. Of those optima, I want to find the optimum that activates (aka, "pegs" or "bumps") the largest number of constraints. Is there a general mechanism to achieve this?
I was able to achieve what I wanted via MIP by duplicating the constraints and adding a binary variable for each of the duplicates -- an "enabler". I then maximize the sum of those. It gives very good results. However, this takes my 30ms LP to two minutes of processing (using Gurobi), and that's not an acceptable delay.