Source code for cvxpy.constraints.exponential

Copyright 2013 Steven Diamond

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

[docs]class ExpCone(Constraint): """A reformulated exponential cone constraint. Operates elementwise on :math:`x, y, z`. Original cone: .. math:: K = \\{(x,y,z) \\mid y > 0, ye^{x/y} <= z\\} \\cup \\{(x,y,z) \\mid x \\leq 0, y = 0, z \\geq 0\\} Reformulated cone: .. math:: K = \\{(x,y,z) \\mid y, z > 0, y\\log(y) + x \\leq y\\log(z)\\} \\cup \\{(x,y,z) \\mid x \\leq 0, y = 0, z \\geq 0\\} Parameters ---------- x : Variable x in the exponential cone. y : Variable y in the exponential cone. z : Variable z in the exponential cone. """ def __init__(self, x, y, z, constr_id=None): self.x = x self.y = y self.z = z super(ExpCone, self).__init__([self.x, self.y, self.z], constr_id) def __str__(self): return "ExpCone(%s, %s, %s)" % (self.x, self.y, self.z) def __repr__(self): return "ExpCone(%s, %s, %s)" % (self.x, self.y, self.z) @property def residual(self): # TODO(akshayka): The projection should be implemented directly. from cvxpy import Problem, Minimize, Variable, norm2, hstack if self.x.value is None or self.y.value is None or self.z.value is None: return None x = Variable(self.x.shape) y = Variable(self.y.shape) z = Variable(self.z.shape) constr = [ExpCone(x, y, z)] obj = Minimize(norm2(hstack([x, y, z]) - hstack([self.x.value, self.y.value, self.z.value]))) problem = Problem(obj, constr) return problem.solve() @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 num_cones(self): """The number of elementwise cones. """ return[0].shape, dtype=int) def cone_sizes(self): """The dimensions of the exponential cones. Returns ------- list A list of the sizes of the elementwise cones. """ return [3]*self.num_cones()
[docs] def is_dcp(self): """An exponential constraint is DCP if each argument 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() def canonicalize(self): """Canonicalizes by converting expressions to LinOps. """ arg_objs = [] arg_constr = [] for arg in self.args: arg_objs.append(arg.canonical_form[0]) arg_constr + arg.canonical_form[1] return 0, [ExpCone(*arg_objs)] + arg_constr