Source code for cvxpy.constraints.psd

Copyright 2013 Steven Diamond

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from cvxpy.constraints.constraint import Constraint
from cvxpy.expressions import cvxtypes
from cvxpy.utilities import scopes

[docs]class PSD(Constraint): """A constraint of the form :math:`\\frac{1}{2}(X + X^T) \\succcurlyeq_{S_n^+} 0` Applying a ``PSD`` constraint to a two-dimensional expression ``X`` constrains its symmetric part to be positive semidefinite: i.e., it constrains ``X`` to be such that .. math:: z^T(X + X^T)z \\geq 0, for all :math:`z`. The preferred way of creating a ``PSD`` constraint is through operator overloading. To constrain an expression ``X`` to be PSD, write ``X >> 0``; to constrain it to be negative semidefinite, write ``X << 0``. Strict definiteness constraints are not provided, as they do not make sense in a numerical setting. Parameters ---------- expr : Expression. The expression to constrain; *must* be two-dimensional. constr_id : int A unique id for the constraint. """ def __init__(self, expr, constr_id=None) -> None: # Argument must be square matrix. if len(expr.shape) != 2 or expr.shape[0] != expr.shape[1]: raise ValueError( "Non-square matrix in positive definite constraint." ) super(PSD, self).__init__([expr], constr_id) def name(self) -> str: return "%s >> 0" % self.args[0]
[docs] def is_dcp(self, dpp: bool = False) -> bool: """A PSD constraint is DCP if the constrained expression is affine. """ if dpp: with scopes.dpp_scope(): return self.args[0].is_affine() return self.args[0].is_affine()
def is_dgp(self, dpp: bool = False) -> bool: return False def is_dqcp(self) -> bool: return self.is_dcp() @property def residual(self): """The residual of the constraint. Returns ------- NumPy.ndarray """ if self.expr.value is None: return None min_eig = cvxtypes.lambda_min()(self.args[0] + self.args[0].T)/2 return cvxtypes.neg()(min_eig).value