Source code for picos.constraints.con_logsumexp

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# Copyright (C) 2018-2019 Maximilian Stahlberg
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"""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())