Originally posted by: Nodame

While solving an optimization problem, I am calling cplex solver from C#. I would like to add some IFTHEN constraints to describe some sort of Indicator variable.

My two variables are x  ( x  takes non negative double values) and y (y is binary: 0 or 1) . I would like a constraint that does the following:

if x > 0 then y = 1 and

if x = 0 then y = 0.

I have tried describing the positiveness of x, but I cannot seem to find a 'STRICTLY' ' Greater Method (the only one I could find was the cplex.Ge()). 

To get around this problem, I tried using two conditions ">=" and "Not="  (Ge and Neq) for expressing ">"  . However  cplex.Neq(x, 0) does not seem to work (gives me an error). Any suggestion to solve this problem would be very appreciated.

So far, this is what I have:

IConstraint positiveX = (cplex.Ge(x, 0)) && (cplex.Neq(x, 0));//the cplex.Neq gives an error
IConstraint oneY = cplex.Eq(y,1) ;
IConstraint zeroX = cplex.Eq(x, 0);
IConstraint zeroY = cplex.Eq(y, 0);

cplex.Add(cplex.IfThen(positiveX, oneY));
cplex.Add(cplex.IfThen(zeroX, zeroY));

It's not possible. Linear and mixed integer linear programs require closed feasible regions. Strict inequalities less to feasible regions that are not closed. The best you can do is replace x>0 with x>= epsilon for some small positive epsilon, and hope that the optimal solution does not have 0<x<epsilon. This is a FAQ. If you search the forum, you'll find answers to it.

Originally posted by: Nodame

Thanks. That works for me.