Source code for picos.constraints.con_sumexp

# ------------------------------------------------------------------------------
# Copyright (C) 2018-2019 Maximilian Stahlberg
# This file is part of PICOS.
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"""Implementation of :class:`SumExponentialsConstraint`."""

import math
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 SumExponentialsConstraint(Constraint): """Upper bound on a sum of exponentials."""
[docs] class ConicConversion(ConstraintConversion): """Sum of exponentials 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.numerator y = con.denominator n = con.theSum.n b = con.upperBound P = Problem() u = P.add_variable("__u", n) P.add_constraint((u | 1) <= b) for i in range(n): P.add_constraint((u[i] // y[i] // x[i]) << ExponentialCone()) return P
[docs] class LogSumExpConversion(ConstraintConversion): """Sum of exponentials to logarithm of the sum constraint conversion."""
[docs] @classmethod def predict(cls, subtype, options): """Implement :meth:`~.constraint.ConstraintConversion.predict`.""" from . import LogSumExpConstraint n = subtype.argdim if subtype.lse_representable: yield ("con", LogSumExpConstraint.make_type(argdim=n), 1) else: # HACK: Return the input constraint type. # TODO: Handle partial subtype support differently, e.g. by # introducing ConstraintConversion.supports. yield ("con", SumExponentialsConstraint.make_type(*subtype), 1)
[docs] @classmethod def convert(cls, con, options): """Implement :meth:`~.constraint.ConstraintConversion.convert`.""" from ..expressions import LogSumExp from ..modeling import Problem x = con.numerator b = con.upperBound P = Problem() if con.lse_representable: P.add_constraint(LogSumExp(x) <= math.log(b.value)) else: # HACK: See predict. P.add_constraint(con) return P
[docs] def __init__(self, theSum, upperBound): """Construct a :class:`SumExponentialsConstraint`. :param ~picos.expressions.SumExponentials theSum: Constrained expression. :param ~picos.expressions.AffineExpression upperBound: Upper bound on the expression. """ from ..expressions import AffineExpression, SumExponentials assert isinstance(theSum, SumExponentials) assert isinstance(upperBound, AffineExpression) assert len(upperBound) == 1 self.theSum = theSum self.upperBound = upperBound super(SumExponentialsConstraint, self).__init__(theSum._typeStr)
@property def numerator(self): """The :math:`x` of the sum.""" return self.theSum.x
[docs] @cached_property def denominator(self): """The :math:`y` of the sum, or :math:`1`.""" if self.theSum.y is None: from ..expressions import AffineExpression return AffineExpression.from_constant(1, self.theSum.x.shape) else: return self.theSum.y
@property def lse_representable(self): """Whether this can be converted to a logarithmic constraint.""" if self.theSum.y is not None: return False if not self.upperBound.constant: return False if self.upperBound.value < 0: return False return True Subtype = namedtuple("Subtype", ("argdim", "lse_representable")) def _subtype(self): return self.Subtype(self.theSum.n, self.lse_representable) @classmethod def _cost(cls, subtype): # NOTE: Twice the argument dimension due to the denominator. return 2*subtype.argdim + 1 def _expression_names(self): yield "theSum" yield "upperBound" def _str(self): return glyphs.le(self.theSum.string, self.upperBound.string) def _get_slack(self): return self.upperBound.safe_value - self.theSum.safe_value
# -------------------------------------- __all__ = api_end(_API_START, globals())