Source code for picos.constraints.con_expcone

# coding: utf-8

# ------------------------------------------------------------------------------
# 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
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# PICOS is distributed in the hope that it will be useful,
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"""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())
# -------------------------------

[docs]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`. """
[docs] 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[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())