Source code for cvxpy.constraints.nonpos

"""

you may not use this file except in compliance with the License.
You may obtain a copy of the License at

Unless required by applicable law or agreed to in writing, software
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
"""

import cvxpy.lin_ops.lin_utils as lu
# Only need Variable from expressions, but that would create a circular import.
from cvxpy.constraints.constraint import Constraint
import numpy as np

[docs]class NonPos(Constraint):
"""A constraint of the form :math:x \\leq 0.

The preferred way of creating a NonPos constraint is through
operator overloading. To constrain an expression x to be non-positive,
simply write x <= 0; to constrain x to be non-negative, write
x >= 0. The former creates a NonPos constraint with x
as its argument, while the latter creates one with -x as its argument.
Strict inequalities are not supported, as they do not make sense in a
numerical setting.

Parameters
----------
expr : Expression
The expression to constrain.
constr_id : int
A unique id for the constraint.
"""
def __init__(self, expr, constr_id=None):
if expr.is_complex():
raise ValueError("Inequality constraints cannot be complex.")
super(NonPos, self).__init__([expr], constr_id)

def name(self):
return "%s <= 0" % self.args

[docs]    def is_dcp(self):
"""A non-positive constraint is DCP if its argument is convex."""
return self.args.is_convex()

def is_dgp(self):
return False

def is_dqcp(self):
return self.args.is_quasiconvex()

def canonicalize(self):
"""Returns the graph implementation of the object.

Marks the top level constraint as the dual_holder,
so the dual value will be saved to the LeqConstraint.

Returns
-------
tuple
A tuple of (affine expression, [constraints]).
"""
obj, constraints = self.args.canonical_form
dual_holder = lu.create_leq(obj, constr_id=self.id)
return (None, constraints + [dual_holder])

@property
def residual(self):
"""The residual of the constraint.

Returns
---------
NumPy.ndarray
"""
if self.expr.value is None:
return None
return np.maximum(self.expr.value, 0)

class Inequality(Constraint):
"""A constraint of the form :math:x \\leq y.

Parameters
----------
expr : Expression
The expression to constrain.
constr_id : int
A unique id for the constraint.
"""
def __init__(self, lhs, rhs, constr_id=None):
self._expr = lhs - rhs
if self._expr.is_complex():
raise ValueError("Inequality constraints cannot be complex.")
super(Inequality, self).__init__([lhs, rhs], constr_id)

def _construct_dual_variables(self, args):
super(Inequality, self)._construct_dual_variables([self._expr])

@property
def expr(self):
return self._expr

def name(self):
return "%s <= %s" % (self.args, self.args)

@property
def shape(self):
"""int : The shape of the constrained expression."""
return self.expr.shape

@property
def size(self):
"""int : The size of the constrained expression."""
return self.expr.size

def is_dcp(self):
"""A non-positive constraint is DCP if its argument is convex."""
return self.expr.is_convex()

def is_dgp(self):
return (self.args.is_log_log_convex() and
self.args.is_log_log_concave())

def is_dqcp(self):
return (
self.is_dcp() or
(self.args.is_quasiconvex() and self.args.is_constant()) or
(self.args.is_constant() and self.args.is_quasiconcave()))

@property
def residual(self):
"""The residual of the constraint.

Returns
---------
NumPy.ndarray
"""
if self.expr.value is None:
return None
return np.maximum(self.expr.value, 0)