el0ps.penalty.L1norm

class el0ps.penalty.L1norm(alpha)

L1-norm BasePenalty penalty function.

The splitting terms are expressed as

\[h_i(x_i) = \alpha|x_i|\]

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(i, lmbd)

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(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(i, lmbd)

Supremum of the set {x in R | self.conjugate(i, x) <= 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.