el0ps.penalty.Bounds¶

class el0ps.penalty.Bounds(x_lb, x_ub)¶

Bound-constraint BasePenalty penalty function.

The splitting terms are expressed as

\[\begin{split}h_i(x_i) = \begin{cases} 0 & \text{if } x^{\text{lb}}_i \leq x_i \leq x^{\text{ub}}_i \\ +\infty & \text{otherwise} \end{cases}\end{split}\]

for some \(x^{\text{lb}}_i < 0\) and \(x^{\text{ub}}_i > 0\).

Parameters:

x_lb: NDArray: Vector or lower bounds.
x_ub: NDArray: Vector of upper bounds.

__init__(x_lb, x_ub)¶

Methods

`__init__`(x_lb, x_ub)
`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`.