Sign of slack variables

[Arthur Delarue]

This is a very simple question, but I couldn't find a straightforward answer online. When you enter an inequality constraint into a Gurobi model, under the hood it seems to rewrite it as an equality constraint with a slack variable.I'm not sure what convention is used for the sign of the slack variable.

For instance, if I have a constraint of the form

x <= y

I don't know if Gurobi reformulates it as

x + z == y, z >= 0

or as

x == y + z, z <= 0

and the same goes for a constraint of the form

x >= y

After optimizing, when I query the value of a nonzero slack variable, will it always be positive or will its sign depend on the direction of the original inequality for which this slack variable was created ?

Thanks for your help!

[Renan Garcia]

The Slack constraint attribute is always non-negative for <= constraints, and non-positive for >= constraints. For example:

  gurobi> setParam('OutputFlag', 0)

  gurobi> m=Model()

  gurobi> x=m.addVar(lb=3, ub=3)

  gurobi> m.update()

  gurobi> c=m.addConstr(x <= 5)

  gurobi> m.optimize()

  gurobi> print c.slack

  2.0

  gurobi> c.sense='>'

  gurobi> c.rhs=1

  gurobi> m.optimize()

  gurobi> print c.slack

  -2.0

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