Documentation

GRBModel::addQConstr()


GRBModel::addQConstr()

Add a quadratic constraint to a model. Multiple signatures are available.

Important note: the algorithms that Gurobi uses to solve quadratically constrained problems can only handle certain types of quadratic constraints. Constraints of the following forms are always accepted:

  • $x^TQx + q^Tx \le b$, where Q is Positive Semi-Definite (PSD)
  • $x^Tx \le y^{2}$, where $x$ is a vector of variables, and $y$ is a non-negative variable (a Second-Order Cone)
  • $x^Tx \le y z$, where $x$ is a vector of variables, and $y$ and $z$ are non-negative variables (a rotated Second-Order Cone)
If you add a constraint that isn't in one of these forms (and Gurobi presolve is unable to transform the constraint into one of these forms), you'll get an error when you try to solve the model. Constraints where the quadratic terms only involve binary variables will always be transformed into one of these forms.

GRBQConstr addQConstr ( const GRBQuadExpr& lhsExpr,
    char sense,
    const GRBQuadExpr& rhsExpr,
    string name="" )
    Add a quadratic constraint to a model.

    Arguments:

    lhsExpr: Left-hand side expression for new quadratic constraint.

    sense: Sense for new quadratic constraint (GRB_LESS_EQUAL or GRB_GREATER_EQUAL).

    rhsExpr: Right-hand side expression for new quadratic constraint.

    name (optional): Name for new constraint.

    Return value:

    New quadratic constraint object.

GRBQConstr addQConstr ( const GRBQuadExpr& lhsExpr,
    char sense,
    GRBVar rhsVar,
    string name="" )
    Add a quadratic constraint to a model.

    Arguments:

    lhsExpr: Left-hand side expression for new quadratic constraint.

    sense: Sense for new quadratic constraint (GRB_LESS_EQUAL or GRB_GREATER_EQUAL).

    rhsVar: Right-hand side variable for new quadratic constraint.

    name (optional): Name for new constraint.

    Return value:

    New quadratic constraint object.

GRBQConstr addQConstr ( GRBTempConstr& tc,
    string name="" )
    Add a quadratic constraint to a model.

    Arguments:

    tc: Temporary constraint object, created using an overloaded comparison operator. See GRBTempConstr for more information.

    name (optional): Name for new constraint.

    Return value:

    New quadratic constraint object.