Constraints

Creating Constraints

Similarly to variables, constraints are easily created and added to a given Model.

Constraints can be created by calling the constructor of the Ctr class and added to a model by means of Model::add or by calling the Model::add_ctr method. See for instance.

Env env;
Model model(env);

Var x_0(env, 0., Inf, Continuous, "x_0");
Var x_1(env, 0., Inf, Continuous, "x_1");
Ctr constraint(env, x_0 + x_1 >= 1);

model.add(x_0);
model.add(x_1);
model.add(constraint);

A more compact version of this code is obtained by making use of the Model::add_vars and Model::add_ctr methods.

Env env;
Model model(env);

const auto x = model.add_vars(Dim<1>(2), 0., Inf, Continuous, "x");
const auto constraint = model.add_ctr(x[0] + x[1] >= 1);

As you can see, a constraint is created using the pattern {expression} {sign} {expression} where

• {sign} is one of <=, >= and ==;

• {expression} is an expression, i.e., an instance of Expr.

Actually, the pattern {expression} {sign} {expression} only creates a “temporary” constraint, i.e., a constraint which is not associated to any model. This is why we need to add it to a model by calling the Model::add_ctr method. Temporary constraints are objects of the class TempCtr. An equivalent code would be.

Env env;
Model model(env);

const auto x = model.add_vars(Dim<1>(2), 0., Inf, Continuous, "x");
const auto temporary_constraint = TempCtr(Row(x[0] + x[1], 1), GreaterThan);

model.add_ctr(temporary_constraint);

Here, we used the class Row to create the row associated to the constraint. The sign of the constraint is specified by the second argument of the constructor of the TempCtr class, and can take values LessThan, GreaterThan and EqualTo.

Accessing Constraints

Information about a given constraint in a model can be accessed by calling the corresponding methods of the model. The type of a constraint can be accessed by calling the Model::get_ctr_type method. The row of a constraint can be accessed by calling the Model::get_ctr_row method.

If a given model has been solved and feasibility could be proved (or better, optimality), the dual value of a constraint can be accessed by calling the Model::get_ctr_dual method. For infeasible models, a Farkas certificate (dual ray) can be accessed by calling the Model::get_ctr_farkas method.

The Model::has method can be used to check if a given constraint is in the model.

The current index of a constraint in the model can be accessed by calling the Model::get_ctr_index method. Beware, however, that the index may change if the model is modified.

For more details, see the Model class.

Modifying Constraints

The type of a constraint can be modified by calling the Ctr::set_ctr_type method. The value of the right-hand side of a constraint can be modified by calling the Ctr::set_rhs method.

The row of a constraint in the model can be modified by calling the Ctr::set_row method. For instance.

Row row;
row.set_rhs(2);
row.linear().set(x, coefficient_for_x_in_constraint);
row.linear().set(y, coefficient_for_y_in_constraint);

constraint.set_ctr_row(constraint, row);

For more details, see the Model class.

Removing Constraints

A constraint can be removed from a model by calling the Model::remove method.