Source code for picos.expressions.cone_rsoc

# ------------------------------------------------------------------------------
# Copyright (C) 2019 Maximilian Stahlberg
# Based on the original picos.expressions module by Guillaume Sagnol.
# 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 <>.
# ------------------------------------------------------------------------------

"""Implements :class:`RotatedSecondOrderCone`."""

import operator
from collections import namedtuple

from .. import glyphs
from ..apidoc import api_end, api_start
from ..caching import cached_property
from ..constraints import RSOCConstraint
from .cone import Cone
from .exp_affine import AffineExpression

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

[docs]class RotatedSecondOrderCone(Cone): r"""The (narrowed or widened) rotated second order cone. .. _rotatedcone: For :math:`n \in \mathbb{Z}_{\geq 3}` and :math:`p \in \mathbb{R}_{> 0}`, represents the convex cone .. math:: \mathcal{R}_{p}^n = \left\{ x \in \mathbb{R}^n ~\middle|~ p x_1 x_2 \geq \sum_{i = 3}^n x_i^2 \land x_1, x_2 \geq 0 \right\}. For :math:`p = 2`, this is the standard rotated second order cone :math:`\mathcal{R}^n` obtained by rotating the :class:`second order cone <picos.SecondOrderCone>` :math:`\mathcal{Q}^n` by :math:`\frac{\pi}{4}` in the :math:`(x_1, x_2)` plane. The default instance of this class has :math:`p = 1`, which can be understood as a narrowed version of the standard cone. This is more convenient for defining the primal problem but it should be noted that :math:`\mathcal{R}_{1}^n` is not self-dual, so working with :math:`p = 2` may seem more natural when the dual problem is of interest. :Dual cone: The dual cone is .. math:: \left(\mathcal{R}_{p}^n\right)^* = \left\{ x \in \mathbb{R}^n ~\middle|~ \frac{4}{p} x_1 x_2 \geq \sum_{i = 2}^n x_i^2 \land x_1, x_2 \geq 0 \right\}=\mathcal{R}_{4/p}^n. The cone is thus self-dual for :math:`p = 2`. """
[docs] def __init__(self, p=1, dim=None): """Construct a rotated second order cone. :param float p: The positive factor :math:`p` in the definition. """ try: p = float(p) except Exception as error: raise TypeError("Failed to load the parameter 'p' as a float.") \ from error if p <= 0: raise ValueError("The parameter 'p' must be positive.") self._p = p if dim and dim < 3: raise ValueError("The minimal dimension for {} is {}." .format(self.__class__.__name__, 3)) typeStr = "Rotated Second Order Cone" if p < 2: typeStr = "Narrowed " + typeStr elif p > 2: typeStr = "Widened " + typeStr symbStr = glyphs.set(glyphs.sep( glyphs.col_vectorize("u", "v", "x"), glyphs.and_( glyphs.le( glyphs.squared(glyphs.norm("x")), glyphs.clever_mul(glyphs.scalar(p), glyphs.mul("u", "v"))),"u", 0)))) Cone.__init__(self, dim, typeStr, symbStr)
@property def p(self): """A narrowing (:math:`p < 2`) or widening (:math:`p > 2`) factor.""" return self._p def _get_mutables(self): return frozenset() def _replace_mutables(self): return self Subtype = namedtuple("Subtype", ("dim",)) def _get_subtype(self): return self.Subtype(self.dim) @classmethod def _predict(cls, subtype, relation, other): assert isinstance(subtype, cls.Subtype) if relation == operator.__rshift__: if issubclass(other.clstype, AffineExpression) \ and not subtype.dim or subtype.dim == other.subtype.dim \ and other.subtype.dim >= 3: return RSOCConstraint.make_type(other.subtype.dim - 2) return Cone._predict_base(cls, subtype, relation, other) def _rshift_implementation(self, element): if isinstance(element, AffineExpression): self._check_dimension(element) if len(element) < 3: raise TypeError("Elements of the rotated second order cone must" " be at least three-dimensional.") element = element.vec return RSOCConstraint(element[2:], self.p * element[0], element[1]) # Handle scenario uncertainty for all cones. return Cone._rshift_base(self, element)
[docs] @cached_property def dual_cone(self): """Implement :attr:`.cone.Cone.dual_cone`.""" return self.__class__(p=(4.0/self._p), dim=self.dim)
# -------------------------------------- __all__ = api_end(_API_START, globals())