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CVXR (version 1.0)

Huber-class: The Huber class.

Description

This class represents the elementwise Huber function, \(Huber(x, M) = \)

  • \(2M|x|-M^2\)for \(|x| \geq |M|\)

  • \(|x|^2\)for \(|x| \leq |M|.\)

Usage

Huber(x, M = 1)
# S4 method for Huber
to_numeric(object, values)
# S4 method for Huber
sign_from_args(object)
# S4 method for Huber
is_atom_convex(object)
# S4 method for Huber
is_atom_concave(object)
# S4 method for Huber
is_incr(object, idx)
# S4 method for Huber
is_decr(object, idx)
# S4 method for Huber
is_quadratic(object)
# S4 method for Huber
get_data(object)
# S4 method for Huber
validate_args(object)
# S4 method for Huber
.grad(object, values)

Arguments

x

An '>Expression object.

M

A positive scalar value representing the threshold. Defaults to 1.

object

A '>Huber object.

values

A list of numeric values for the arguments

idx

An index into the atom.

Methods (by generic)

  • to_numeric: The Huber function evaluted elementwise on the input value.

  • sign_from_args: The atom is positive.

  • is_atom_convex: The atom is convex.

  • is_atom_concave: The atom is not concave.

  • is_incr: A logical value indicating whether the atom is weakly increasing.

  • is_decr: A logical value indicating whether the atom is weakly decreasing.

  • is_quadratic: The atom is quadratic if x is affine.

  • get_data: A list containing the parameter M.

  • validate_args: Check that M is a non-negative constant.

  • .grad: Gives the (sub/super)gradient of the atom w.r.t. each variable

Slots

x

An '>Expression or numeric constant.

M

A positive scalar value representing the threshold. Defaults to 1.