Source code for cvxpy.constraints.second_order

"""
Copyright 2013 Steven Diamond

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""

from cvxpy.constraints.constraint import Constraint
import numpy as np


[docs]class SOC(Constraint): """A second-order cone constraint for each row/column. Assumes ``t`` is a vector the same length as ``X``'s columns (rows) for ``axis == 0`` (``1``). Attributes: t: The scalar part of the second-order constraint. X: A matrix whose rows/columns are each a cone. axis: Slice by column 0 or row 1. """ def __init__(self, t, X, axis=0, constr_id=None): # TODO allow imaginary X. assert not t.shape or len(t.shape) == 1 self.axis = axis super(SOC, self).__init__([t, X], constr_id) def __str__(self): return "SOC(%s, %s)" % (self.args[0], self.args[1]) @property def residual(self): t = self.args[0].value X = self.args[1].value if t is None or X is None: return None if self.axis == 0: X = X.T norms = np.linalg.norm(X, ord=2, axis=1) zero_indices = np.where(X <= -t)[0] averaged_indices = np.where(X >= np.abs(t))[0] X_proj = np.array(X) t_proj = np.array(t) X_proj[zero_indices] = 0 t_proj[zero_indices] = 0 avg_coeff = 0.5 * (1 + t/norms) X_proj[averaged_indices] = avg_coeff * X[averaged_indices] t_proj[averaged_indices] = avg_coeff * t[averaged_indices] return np.linalg.norm(np.concatenate([X, t], axis=1) - np.concatenate([X_proj, t_proj], axis=1), ord=2, axis=1) def get_data(self): """Returns info needed to reconstruct the object besides the args. Returns ------- list """ return [self.axis] def num_cones(self): """The number of elementwise cones. """ return np.prod(self.args[0].shape, dtype=int) @property def size(self): """The number of entries in the combined cones. """ # TODO use size of dual variable(s) instead. return sum(self.cone_sizes()) def cone_sizes(self): """The dimensions of the second-order cones. Returns ------- list A list of the sizes of the elementwise cones. """ cones = [] cone_size = 1 + self.args[1].shape[self.axis] for i in range(self.num_cones()): cones.append(cone_size) return cones
[docs] def is_dcp(self): """An SOC constraint is DCP if each of its arguments is affine. """ return all(arg.is_affine() for arg in self.args)
def is_dgp(self): return False def is_dqcp(self): return self.is_dcp() # TODO hack def canonicalize(self): t, t_cons = self.args[0].canonical_form X, X_cons = self.args[1].canonical_form new_soc = SOC(t, X, self.axis) return (None, [new_soc] + t_cons + X_cons)