addQConstr ( lhs, sense=None, rhs=None, name="" )

Add a quadratic constraint to a model.

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:

  • <span>$</span>x^TQx + q^Tx \le b<span>$</span>, where <span>$</span>Q<span>$</span> is Positive Semi-Definite (PSD)
  • <span>$</span>x^Tx \le y^{2}<span>$</span>, where <span>$</span>x<span>$</span> is a vector of variables, and <span>$</span>y<span>$</span> is a non-negative variable (a Second-Order Cone)
  • <span>$</span>x^Tx \le y z<span>$</span>, where <span>$</span>x<span>$</span> is a vector of variables, and <span>$</span>y<span>$</span> and <span>$</span>z<span>$</span> 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.

Note that this method also accepts a TempConstr as its first argument (with the name as its second argument). This allows you to use operator overloading to create constraints. See TempConstr for more information.


lhs: Left-hand side for new quadratic constraint. Can be a constant, a Var, a LinExpr, or a QuadExpr.

sense: Sense for new quadratic constraint (GRB.LESS_EQUAL or GRB.GREATER_EQUAL).

rhs: Right-hand side for new quadratic constraint. Can be a constant, a Var, a LinExpr, or a QuadExpr.

name: Name for new constraint. Note that name will be stored as an ASCII string. Thus, a name like 'A<span>$</span>{\rightarrow}<span>$</span>B' will produce an error, because '<span>$</span>{\rightarrow}<span>$</span>' can not be represented as an ASCII character. Note also that names that contain spaces are strongly discouraged, because they can't be written to LP format files.

Return value:

New quadratic constraint object.

Example usage:

  model.addQConstr(x*x + y*y, GRB.LESS_EQUAL, z*z, "c0")
  model.addQConstr(x*x + y*y <= 2.0, "c1")