Indicator constraints in the Interactive Optimizer

Contrasts indicator constraints with a Big M formulation in the Interactive Optimizer.

In the Interactive Optimizer, you can include indicator constraints among the usual linear constraints in LP-file format. You can also use the commands enter and add with indicator constraints. For example, you could declare y as a binary variable and enter the following:

constr01: y = 0 -> x1 + x2 + x3 = 0 

In plain English, that indicator constraint states that if y is 0 (zero), then x1 + x2 + x3 must be 0 (zero). Likewise, if x1 + x2 + x3 is not 0 (zero), then y must be 1 (one).

That formulation of an indicator constraint is recommended instead of the following Big M formulation:

constr01: x1 + x2 + x3 - 1e+9 y <= 0 // not recommended

That Big M formulation relies on the x values summing to less than the Big M value (in this case, one billion). Such an assumption may cause numeric instability or undesirable solutions in certain circumstances, whereas a model with the indicator constraint, by contrast, introduces no new assumptions about upper bounds. In that respect, the use of indicator constraints instead of a Big M formulation offers a more numerically stable model, closer to the mathematical programming issues of the problem, and thus more likely to produce useful solutions of the problem.