Constraint¶
The Constraint
class is used to define a constraint in the optimization model. It is a subclass
of Expression
and has the same methods and properties as Expression
.
PyOptInterface supports the following types of constraints:
Linear Constraint
Quadratic Constraint
Second-Order Cone Constraint
Special Ordered Set (SOS) Constraint
Note
Not all optimizers support all types of constraints. Please refer to the documentation of the optimizer you are using to see which types of constraints are supported.
import pyoptinterface as poi
from pyoptinterface import copt
model = copt.Model()
2024-10-09 14:02:37 [INFO] checks license for COPT v7.1.4 20240627
2024-10-09 14:02:37 [WARN] no license files in current working folder: /home/runner/work/PyOptInterface/PyOptInterface/docs/source
2024-10-09 14:02:37 [WARN] no license files in binary folder: /opt/hostedtoolcache/Python/3.11.10/x64/bin
2024-10-09 14:02:37 [WARN] no license files in HOME folder: /home/runner/copt
2024-10-09 14:02:37 [INFO] empty environment variable: COPT_LICENSE_DIR
2024-10-09 14:02:37 [WARN] no license files in EV 'COPT_LICENSE_DIR':
No license found. Starting COPT with size limitations for non-commercial use
Please apply for a license from www.shanshu.ai/copt
Linear Constraint¶
It is defined as:
It can be added to the model using the add_linear_constraint
method of the Model
class.
x = model.add_variable(name="x")
y = model.add_variable(name="y")
con = model.add_linear_constraint(2.0*x + 3.0*y, poi.ConstraintSense.LessEqual, 1.0)
- model.add_linear_constraint(expr, sense, rhs[, name=""])¶
add a linear constraint to the model
- Parameters:
expr – the expression of the constraint
sense (pyoptinterface.ConstraintSense) – the sense of the constraint, which can be
GreaterEqual
,Equal
, orLessEqual
rhs (float) – the right-hand side of the constraint
name (str) – the name of the constraint, optional
- Returns:
the handle of the constraint
Note
PyOptInterface provides pyoptinterface.Eq
, pyoptinterface.Leq
, and pyoptinterface.Geq
as alias of pyoptinterface.ConstraintSense
to represent the sense of the constraint with a shorter name.
Quadratic Constraint¶
Like the linear constraint, it is defined as:
It can be added to the model using the add_quadratic_constraint
method of the Model
class.
x = model.add_variable(name="x")
y = model.add_variable(name="y")
expr = x*x + 2.0*x*y + 4.0*y*y
con = model.add_quadratic_constraint(expr, poi.ConstraintSense.LessEqual, 1.0)
- model.add_quadratic_constraint(expr, sense, rhs[, name=""])¶
add a quadratic constraint to the model
- Parameters:
expr – the expression of the constraint
sense (pyoptinterface.ConstraintSense) – the sense of the constraint, which can be
GreaterEqual
,Equal
, orLessEqual
rhs (float) – the right-hand side of the constraint
name (str) – the name of the constraint, optional
- Returns:
the handle of the constraint
Second-Order Cone Constraint¶
It is defined as:
It can be added to the model using the add_second_order_cone_constraint
method of the Model
class.
N = 6
vars = [model.add_variable() for i in range(N)]
con = model.add_second_order_cone_constraint(vars)
There is another form of second-order cone constraint called as rotated second-order cone constraint, which is defined as:
- model.add_second_order_cone_constraint(variables[, name="", rotated=False])¶
add a second order cone constraint to the model
- Parameters:
variables – the variables of the constraint, can be a list of variables
name (str) – the name of the constraint, optional
rotated (bool) – whether the constraint is a rotated second-order cone constraint, optional
- Returns:
the handle of the constraint
Exponential Cone Constraint¶
It is defined as:
The dual form is:
Currently, only COPT(after 7.1.4), Mosek support exponential cone constraint. It can be added to the model using the add_exp_cone_constraint
method of the Model
class.
- model.add_exp_cone_constraint(variables[, name="", dual=False])¶
add a second order cone constraint to the model
- Parameters:
variables – the variables of the constraint, can be a list of variables
name (str) – the name of the constraint, optional
dual (bool) – whether the constraint is dual form of exponential cone, optional
- Returns:
the handle of the constraint
Special Ordered Set (SOS) Constraint¶
SOS constraints are used to model special structures in the optimization problem.
It contains two types: SOS1
and SOS2
, the details can be found in Wikipedia.
It can be added to the model using the add_sos_constraint
method of the Model
class.
N = 6
vars = [model.add_variable(domain=poi.VariableDomain.Binary) for i in range(N)]
con = model.add_sos_constraint(vars, poi.SOSType.SOS1)
- model.add_sos_constraint(variables, sos_type[, weights])¶
add a special ordered set constraint to the model
- Parameters:
variables – the variables of the constraint, can be a list of variables
sos_type (pyoptinterface.SOSType) – the type of the SOS constraint, which can be
SOS1
orSOS2
weights (list[float]) – the weights of the variables, optional, will be set to 1 if not provided
- Returns:
the handle of the constraint
Constraint Attributes¶
After a constraint is created, we can query or modify its attributes. The following table lists the standard constraint attributes:
Attribute name |
Type |
---|---|
Name |
str |
Primal |
float |
Dual |
float |
The most common attribute we will use is the Dual
attribute, which represents the dual multiplier of the constraint after optimization.
# get the dual multiplier of the constraint after optimization
dual = model.get_constraint_attribute(con, poi.ConstraintAttribute.Dual)
Delete constraint¶
We can delete a constraint by calling the delete_constraint
method of the model:
model.delete_constraint(con)
After a constraint is deleted, it cannot be used in the model anymore, otherwise an exception will be raised.
We can query whether a constraint is active by calling the is_constraint_active
method of the
model:
is_active = model.is_constraint_active(con)
Modify constraint¶
For linear and quadratic constraints, we can modify the right-hand side of a constraint by
calling the set_normalized_rhs
method of the model.
For linear constraints, we can modify the coefficients of the linear part of the constraint by
calling the set_normalized_coefficient
method of the model.
con = model.add_linear_constraint(x + y, poi.Leq, 1.0)
# modify the right-hand side of the constraint
model.set_normalized_rhs(con, 2.0)
# modify the coefficient of the linear part of the constraint
model.set_normalized_coefficient(con, x, 2.0)