EyeMinusInv-class {CVXR}

The EyeMinusInv class.

Description

This class represents the unity resolvent of an elementwise positive matrix X, i.e., (I - X)^{-1}, and it enforces the constraint that the spectral radius of X is at most 1. This atom is log-log convex.

Usage

EyeMinusInv(X)

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

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

## S4 method for signature 'EyeMinusInv'
dim_from_args(object)

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

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

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

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

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

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

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

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

Arguments

X

An Expression or numeric matrix.

object, x

An EyeMinusInv object.

values

A list of numeric values for the arguments

idx

An index into the atom.

Methods (by generic)

• to_numeric(EyeMinusInv): The unity resolvent of the matrix.

• name(EyeMinusInv): The name and arguments of the atom.

• dim_from_args(EyeMinusInv): The dimensions of the atom determined from its arguments.

• sign_from_args(EyeMinusInv): The (is positive, is negative) sign of the atom.

• is_atom_convex(EyeMinusInv): Is the atom convex?

• is_atom_concave(EyeMinusInv): Is the atom concave?

• is_atom_log_log_convex(EyeMinusInv): Is the atom log-log convex?

• is_atom_log_log_concave(EyeMinusInv): Is the atom log-log concave?

• is_incr(EyeMinusInv): Is the atom weakly increasing in the index?

• is_decr(EyeMinusInv): Is the atom weakly decreasing in the index?

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

Slots

X

An Expression or numeric matrix.