Originally posted by: Nodame

I am trying to Linearize an IF/THEN constraint to improve Performance of cplex Solver (I am calling cplex from C#).

I would like to define an Indicator Variable B:

If x >0 then B = 1

If x <=0 then B = 0.

(where  B is Binary and x is real)

My attempt for the second IF/THEN constraint was : 

x <= B * M (where M is a very large Negative number). This works if x <=0, however, this Linear constraint does not hold anymore if x >0.

I would like to have LINEAR constraint(s) that will do the job for both IF/THEN constraints.

You cannot do exactly what you want; the strict inequality x > 0 is a problem (mathematically, not just with CPLEX). What you can do is select a small positive epsilon (but large enough that it does not look like 0 when a bit of rounding error piles up) and use the constraints x <= M * B, x >= epsilon - M * (1 - B).

Originally posted by: Nodame

Makes sense. Thanks!