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Power-class

The Power class.


Description

This class represents the elementwise power function f(x) = x^p. If expr is a CVXR expression, then expr^p is equivalent to Power(expr, p).

Usage

Power(x, p, max_denom = 1024)

## S4 method for signature 'Power'
to_numeric(object, values)

## S4 method for signature 'Power'
sign_from_args(object)

## S4 method for signature 'Power'
is_atom_convex(object)

## S4 method for signature 'Power'
is_atom_concave(object)

## S4 method for signature 'Power'
is_atom_log_log_convex(object)

## S4 method for signature 'Power'
is_atom_log_log_concave(object)

## S4 method for signature 'Power'
is_constant(object)

## S4 method for signature 'Power'
is_incr(object, idx)

## S4 method for signature 'Power'
is_decr(object, idx)

## S4 method for signature 'Power'
is_quadratic(object)

## S4 method for signature 'Power'
is_qpwa(object)

## S4 method for signature 'Power'
.grad(object, values)

## S4 method for signature 'Power'
.domain(object)

## S4 method for signature 'Power'
get_data(object)

## S4 method for signature 'Power'
copy(object, args = NULL, id_objects = list())

## S4 method for signature 'Power'
name(x)

Arguments

x

The Expression to be raised to a power.

p

A numeric value indicating the scalar power.

max_denom

The maximum denominator considered in forming a rational approximation of p.

object

A Power object.

values

A list of numeric values for the arguments

idx

An index into the atom.

args

A list of arguments to reconstruct the atom. If args=NULL, use the current args of the atom

id_objects

Currently unused.

Details

For p = 0, f(x) = 1, constant, positive.

For p = 1, f(x) = x, affine, increasing, same sign as x.

For p = 2,4,8,..., f(x) = |x|^p, convex, signed monotonicity, positive.

For p < 0 and f(x) =

  • x^p for x > 0

  • +∞x ≤q 0

, this function is convex, decreasing, and positive.

For 0 < p < 1 and f(x) =

  • x^p for x ≥q 0

  • -∞x < 0

, this function is concave, increasing, and positive.

For p > 1, p \neq 2,4,8,… and f(x) =

  • x^p for x ≥q 0

  • +∞x < 0

, this function is convex, increasing, and positive.

Methods (by generic)

  • to_numeric: Throw an error if the power is negative and cannot be handled.

  • sign_from_args: The sign of the atom.

  • is_atom_convex: Is p ≤q 0 or p ≥q 1?

  • is_atom_concave: Is p ≥q 0 or p ≤q 1?

  • is_atom_log_log_convex: Is the atom log-log convex?

  • is_atom_log_log_concave: Is the atom log-log concave?

  • is_constant: A logical value indicating whether the atom is constant.

  • 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: A logical value indicating whether the atom is quadratic.

  • is_qpwa: A logical value indicating whether the atom is quadratic of piecewise affine.

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

  • .domain: Returns constraints describng the domain of the node

  • get_data: A list containing the output of pow_low, pow_mid, or pow_high depending on the input power.

  • copy: Returns a shallow copy of the power atom

  • name: Returns the expression in string form.

Slots

x

The Expression to be raised to a power.

p

A numeric value indicating the scalar power.

max_denom

The maximum denominator considered in forming a rational approximation of p.


CVXR

Disciplined Convex Optimization

v1.0-10
Apache License 2.0 | file LICENSE
Authors
Anqi Fu [aut, cre], Balasubramanian Narasimhan [aut], David W Kang [aut], Steven Diamond [aut], John Miller [aut], Stephen Boyd [ctb], Paul Kunsberg Rosenfield [ctb]
Initial release

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