Norm Uncertainty¶

class lropt.Norm(dimension=None, p=2, rho=1.0, a=None, b=None, c=None, d=None, data=None, ub=None, lb=None, sum_eq=None)¶

Norm uncertainty set, defined as

\[\mathcal{U}_{\text{Norm}} = \{Az+b \ | \ z\| \|_p \le \rho\}\]

when \(p = 2\) this is an ellipsoidal set, and when \(p = \infty\) this is a box set

Parameters¶

rhofloat, optional: Default 1.0.
pinteger, optional: Order of the norm. Default 2.
Anp.array, optional: matrix defining \(A\) in uncertainty set definition. By default \(A = I\)
bnp.array, optional: vector defining \(b\) in uncertainty set definition. By default \(b = 0\)
data: np.array, optional: An array of uncertainty realizations, where each row is one realization. Required if the uncertainty should be trained.
c: np.array, optional: matrix defining the lhs of the polyhedral support: :math: cu le d. By default None.
d: np.array, optional: vector defining the rhs of the polyhedral support: :math: cu le d. By default None.
ub: np.array | float, optional: vector or float defining the upper bound of the support. If scalar, broadcast to a vector. By default None.
lb: np.array | float, optional: vector or float defining the lower bound of the support. If scalar, broadcast to a vector. By default None.
sum_eq: np.array | float, optinal: vector or float defining an equality constraint for the uncertain vector. By default None.