el0ps.penalty.BigmPositiveL2norm

class el0ps.penalty.BigmPositiveL2norm(M, beta)

Positive big-M plus L2-norm BasePenalty penalty function.

The splitting terms are expressed as

\[\begin{split}h_i(x_i) = \begin{cases} \beta x_i^2 & \text{if } 0 \leq x_i \leq M \\ +\infty & \text{otherwise} \end{cases}\end{split}\]

for some \(M > 0\) and \(\beta > 0\).

Parameters:

M: float

Big-M value.

beta: float

L2-norm weight.

__init__(M, beta)

Methods

__init__(M, beta)
bind_model(model)	Impose an constraint associated with the penalty function in a pyomo model.
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.