ExpCone-class: The ExpCone class.

In cvxgrp/CVXR: Disciplined Convex Optimization

The ExpCone class.

Description

This class represents a reformulated exponential cone constraint operating elementwise on a, b, c.

Usage

ExpCone(x, y, z, id = NA_integer_)

## S4 method for signature 'ExpCone'
as.character(x)

## S4 method for signature 'ExpCone'
residual(object)

## S4 method for signature 'ExpCone'
size(object)

## S4 method for signature 'ExpCone'
num_cones(object)

## S4 method for signature 'ExpCone'
cone_sizes(object)

## S4 method for signature 'ExpCone'
is_dcp(object)

## S4 method for signature 'ExpCone'
is_dgp(object)

## S4 method for signature 'ExpCone'
canonicalize(object)

Arguments

x	The variable x in the exponential cone.
y	The variable y in the exponential cone.
z	The variable z in the exponential cone.
id	(Optional) A numeric value representing the constraint ID.
object	A ExpCone object.

Details

Original cone:

K = \{(x,y,z) | y > 0, ye^{x/y} \leq z\} \cup \{(x,y,z) | x \leq 0, y = 0, z \geq 0\}

Reformulated cone:

K = \{(x,y,z) | y, z > 0, y\log(y) + x \leq y\log(z)\} \cup \{(x,y,z) | x \leq 0, y = 0, z \geq 0\}

Methods (by generic)

• residual(ExpCone): The size of the x argument.

• size(ExpCone): The number of entries in the combined cones.

• num_cones(ExpCone): The number of elementwise cones.

• cone_sizes(ExpCone): The dimensions of the exponential cones.

• is_dcp(ExpCone): An exponential constraint is DCP if each argument is affine.

• is_dgp(ExpCone): Is the constraint DGP?

• canonicalize(ExpCone): Canonicalizes by converting expressions to LinOps.

Slots

x

The variable x in the exponential cone.

y

The variable y in the exponential cone.

z

The variable z in the exponential cone.

cvxgrp/CVXR documentation built on Nov. 8, 2024, 5:47 p.m.