Source code for cvxpy.constraints.nonpos

"""
Copyright 2013 Steven Diamond

This file is part of CVXPY.

CVXPY is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

CVXPY is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with CVXPY.  If not, see <http://www.gnu.org/licenses/>.
"""

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[0]
[docs] def is_dcp(self): """A non-positive constraint is DCP if its argument is convex.""" return self.args[0].is_convex()
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[0].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)