sporco.pgm.momentum

Momentum coefficient options for PGM algorithms

Classes

MomentumBase()	Base class for computing momentum coefficient for accelerated proximal gradient method.
MomentumNesterov()	Nesterov's momentum coefficient [6]
MomentumLinear([b])	Linear momentum coefficient [14]
MomentumGenLinear([a, b])	Generalized linear momentum coefficient [40]

Class Descriptions

class sporco.pgm.momentum.MomentumBase

Bases: object

Base class for computing momentum coefficient for accelerated proximal gradient method.

This class is intended to be a base class of other classes that specialise to specific momentum coefficient options.

After termination of the update method the new momentum coefficient is returned.

update()

Update momentum coefficient.

Overriding this method is required.

class sporco.pgm.momentum.MomentumNesterov

Bases: sporco.pgm.momentum.MomentumBase

Nesterov’s momentum coefficient [6]

Applies the update

\[t^{(k+1)} = \frac{1}{2} \left( 1 + \sqrt{1 + 4 \; (t^{(k)})^2} \right) \;,\]

with \(k\) iteration.

update(t)

Update momentum coefficient

class sporco.pgm.momentum.MomentumLinear(b=2.0)

Bases: sporco.pgm.momentum.MomentumBase

Linear momentum coefficient [14]

Applies the update

\[t^{(k+1)} = \frac{k + b}{b} \;,\]

with \(b\) corresponding to a positive constant such that \(b \geq 2\) and \(k\) iteration.

Parameters

bfloat

Summand in numerator and factor in denominator of update.

update(k)

Update momentum coefficient

class sporco.pgm.momentum.MomentumGenLinear(a=50.0, b=2.0)

Bases: sporco.pgm.momentum.MomentumBase

Generalized linear momentum coefficient [40]

Applies the update

\[t^{(k+1)} = \frac{k + a}{b} \;,\]

with \(a, b\) corresponding to postive constants such that \(a \geq b - 1\) and \(b \geq 2\), and \(k\) iteration.

Parameters

afloat

Summand in numerator of update.

bfloat

Factor in denominator of update.

update(k)

Update momentum coefficient