# ------------------------------------------------------------------------------
# Copyright (C) 2018-2019 Maximilian Stahlberg
#
# This file is part of PICOS.
#
# PICOS 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.
#
# PICOS 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
# this program. If not, see <http://www.gnu.org/licenses/>.
# ------------------------------------------------------------------------------
"""Implementation of :class:`LogSumExpConstraint`."""
from collections import namedtuple
from .. import glyphs
from ..apidoc import api_end, api_start
from ..caching import cached_property
from .constraint import Constraint, ConstraintConversion
_API_START = api_start(globals())
# -------------------------------
[docs]class LogSumExpConstraint(Constraint):
"""Upper bound on a logarithm of a sum of exponentials."""
[docs] class ExpConeConversion(ConstraintConversion):
"""Bound on a log-sum-exp to exponential cone constraint conversion."""
[docs] @classmethod
def predict(cls, subtype, options):
"""Implement :meth:`~.constraint.ConstraintConversion.predict`."""
from ..expressions import RealVariable
from . import AffineConstraint, ExpConeConstraint
n = subtype.argdim
yield ("var", RealVariable.make_var_type(dim=n, bnd=0), 1)
yield ("con", AffineConstraint.make_type(dim=1, eq=False), 1)
yield ("con", ExpConeConstraint.make_type(), n)
[docs] @classmethod
def convert(cls, con, options):
"""Implement :meth:`~.constraint.ConstraintConversion.convert`."""
from ..expressions import ExponentialCone
from ..modeling import Problem
x = con.lse.x
n = con.lse.n
b = con.ub
P = Problem()
u = P.add_variable("__u", n)
P.add_constraint((u | 1) <= 1)
for i in range(n):
P.add_constraint((u[i] // 1 // (x[i] - b)) << ExponentialCone())
return P
[docs] @classmethod
def dual(cls, auxVarPrimals, auxConDuals, options):
"""Implement :meth:`~.constraint.ConstraintConversion.dual`."""
# TODO: Verify that this is the dual.
return auxConDuals[0]
[docs] def __init__(self, lse, upperBound):
"""Construct a :class:`LogSumExpConstraint`.
:param ~picos.expressions.LogSumExp lse:
Constrained expression.
:param ~picos.expressions.AffineExpression upperBound:
Upper bound on the expression.
"""
from ..expressions import AffineExpression, LogSumExp
assert isinstance(lse, LogSumExp)
assert isinstance(upperBound, AffineExpression)
assert len(upperBound) == 1
self.lse = lse
self.ub = upperBound
super(LogSumExpConstraint, self).__init__(
lse._typeStr if isinstance(lse, LogSumExp) else "LSE")
@property
def exponents(self):
"""The affine exponents of the bounded log-sum-exp expression."""
return self.lse.x
[docs] @cached_property
def le0(self):
"""The :class:`~.exp_logsumexp.LogSumExp` posed to be at most zero."""
from ..expressions import LogSumExp
if self.ub.is0:
return self.lse
else:
return LogSumExp(self.lse.x - self.ub)
Subtype = namedtuple("Subtype", ("argdim",))
def _subtype(self):
return self.Subtype(self.lse.n)
@classmethod
def _cost(cls, subtype):
return subtype.argdim + 1
def _expression_names(self):
yield "lse"
yield "ub"
def _str(self):
return glyphs.le(self.lse.string, self.ub.string)
def _get_size(self):
return (1, 1)
def _get_slack(self):
return self.ub.safe_value - self.lse.safe_value
# --------------------------------------
__all__ = api_end(_API_START, globals())