el0ps.penalty.PositiveL1norm

class el0ps.penalty.PositiveL1norm(alpha)

Positive L1-norm BasePenalty penalty function.

The splitting terms are expressed as

\[\begin{split}h_i(x_i) = \begin{cases} \alpha x_i & \text{if } x_i \geq 0 \\ +\infty & \text{otherwise} \end{cases}\end{split}\]

for some \(\alpha > 0\).

Parameters:

alpha: float

L1-norm weight.

__init__(alpha)

Methods

__init__(alpha)
conjugate(i, x)	Value of the convex conjugate of the i-th splitting term of the penalty function at x.
conjugate_subdiff(i, x)	Subdifferential of the conjugate of the i-th splitting term of the penalty function at x, returned as an interval.
get_spec()	Specify the numba types of the class attributes.
param_bndry_neg(i, lmbd)	Infimum of the set self.subdiff(i, tau) where tau = self.param_limit_neg(i, lmbd).
param_bndry_pos(i, lmbd)	Supremum of the set self.subdiff(i, tau) where tau = self.param_limit_pos(i, lmbd).
param_limit_neg(i, lmbd)	Infimum of the set self.conjugate_subdiff(i, tau) where tau = self.param_slope_neg(i, lmbd).
param_limit_pos(i, lmbd)	Supremum of the set self.conjugate_subdiff(i, tau) where tau = self.param_slope_pos(i, lmbd).
param_slope_neg(i, lmbd)	Infimum of the set {x in R | self.conjugate(i, x) <= lmbd}.
param_slope_pos(i, lmbd)	Supremum of the set {x in R | self.conjugate(i, x) <= lmbd}.
params_to_dict()	Returns the parameters name and value used to initialize the class instance.
prox(i, x, eta)	Proximity operator of the i-th splitting term of the penalty function weighted by eta at x.
subdiff(i, x)	Subdifferential of the i-th splitting term of the penalty function at x, returned as an interval.
value(i, x)	Value of the i-th splitting term of the penalty function at x.