This is (hopefully) an easy answer but I haven't dealt with this before.
I have a MILP which includes an unbounded, continuous decision variable. However, I generally don't want this decision variable to take negative values, so I want to include a penalty in the objective function where there is zero penalty incurred for a positive value, but for negative values, the penalty is proportional to the absolute value. Basically, I want a value of -100 to be penalized twice as much as -50, and 10x as much as -10.
Right now I have formulated an indicator variable that is 1 if the decision variable is negative, which incurs a penalty; but this penalty is the same for any negative value.
Any suggestions on how to implement this?