Source code for picos.constraints.con_expcone

# ------------------------------------------------------------------------------
# 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:`ExpConeConstraint`."""

from collections import namedtuple

import numpy

from .. import glyphs
from ..apidoc import api_end, api_start
from ..caching import cached_property
from .constraint import Constraint

_API_START = api_start(globals())
# -------------------------------


class ExpConeConstraint(Constraint):
    r"""Exponential cone membership constraint.

    An exponential cone constraint stating that :math:`(x, y, z)` fulfills
    :math:`x \geq y e^{\frac{z}{y}} \land x > 0 \land y > 0`.
    """

    def __init__(self, element, customString=None):
        """Construct an :class:`ExpConeConstraint`.

        :param ~picos.expressions.AffineExpression element:
            Three-dimensional expression representing the vector
            :math:`(x, y, z)`.
        :param str customString:
            Optional string description.
        """
        from ..expressions import AffineExpression

        assert isinstance(element, AffineExpression)
        assert len(element) == 3

        self.element = element

        super(ExpConeConstraint, self).__init__(
            "Exponential Cone", customString, printSize=False)

    x = property(lambda self: self.element[0])
    y = property(lambda self: self.element[1])
    z = property(lambda self: self.element[2])

    @cached_property
    def conic_membership_form(self):
        """Implement for :class:`~.constraint.ConicConstraint`."""
        from ..expressions import ExponentialCone
        return self.element.vec, ExponentialCone()

    Subtype = namedtuple("Subtype", ())

    def _subtype(self):
        return self.Subtype()

    @classmethod
    def _cost(cls, subtype):
        return 3

    def _expression_names(self):
        yield "element"

    def _str(self):
        return glyphs.ge(self.element[0].string,
            glyphs.mul(self.element[1].string, glyphs.exp(glyphs.div(
            self.element[2].string, self.element[1].string))))

    def _get_size(self):
        return (3, 1)

    def _get_slack(self):
        x = self.element.safe_value

        # TODO: Also consider x_1 > 0 and x_2 > 0 by projecting x on the cone's
        #       surface and measuring the distance between the projection and x.
        return x[0] - x[1] * numpy.exp(x[2] / x[1])


# --------------------------------------
__all__ = api_end(_API_START, globals())