AugLagrangianFunction< LagrangianFunction > Class Template Reference

This is a utility class used by AugLagrangian, meant to wrap a LagrangianFunction into a function usable by a simple optimizer like L-BFGS. More...

Public Member Functions
	AugLagrangianFunction (LagrangianFunction &function)
	Initialize the AugLagrangianFunction, but don't set the Lagrange multipliers or penalty parameters yet. More...
	AugLagrangianFunction (LagrangianFunction &function, const arma::vec &lambda, const double sigma)
	Initialize the AugLagrangianFunction with the given LagrangianFunction, Lagrange multipliers, and initial penalty parameter. More...
double	Evaluate (const arma::mat &coordinates) const
	Evaluate the objective function of the Augmented Lagrangian function, which is the standard Lagrangian function evaluation plus a penalty term, which penalizes unsatisfied constraints. More...
template < >
double	Evaluate (const arma::mat &coordinates) const
template < >
double	Evaluate (const arma::mat &coordinates) const
const LagrangianFunction &	Function () const
	Get the Lagrangian function. More...
LagrangianFunction &	Function ()
	Modify the Lagrangian function. More...
const arma::mat &	GetInitialPoint () const
	Get the initial point of the optimization (supplied by the LagrangianFunction). More...
void	Gradient (const arma::mat &coordinates, arma::mat &gradient) const
	Evaluate the gradient of the Augmented Lagrangian function. More...
template < >
void	Gradient (const arma::mat &coordinates, arma::mat &gradient) const
template < >
void	Gradient (const arma::mat &coordinates, arma::mat &gradient) const
const arma::vec &	Lambda () const
	Get the Lagrange multipliers. More...
arma::vec &	Lambda ()
	Modify the Lagrange multipliers. More...
double	Sigma () const
	Get sigma (the penalty parameter). More...
double &	Sigma ()
	Modify sigma (the penalty parameter). More...

Detailed Description

template

<

typename

LagrangianFunction

>

class mlpack::optimization::AugLagrangianFunction< LagrangianFunction >

This is a utility class used by AugLagrangian, meant to wrap a LagrangianFunction into a function usable by a simple optimizer like L-BFGS.

Given a LagrangianFunction which follows the format outlined in the documentation for AugLagrangian, this class provides Evaluate(), Gradient(), and GetInitialPoint() functions which allow this class to be used with a simple optimizer like L-BFGS.

This class can be specialized for your particular implementation – commonly, a faster method for computing the overall objective and gradient of the augmented Lagrangian function can be implemented than the naive, default implementation given. Use class template specialization and re-implement all of the methods (unfortunately, C++ specialization rules mean you have to re-implement everything).

Template Parameters

LagrangianFunction

Lagrangian function to be used.

Definition at line 38 of file aug_lagrangian_function.hpp.

Constructor & Destructor Documentation

AugLagrangianFunction() [1/2]

AugLagrangianFunction

(

LagrangianFunction &

function

)

Initialize the AugLagrangianFunction, but don't set the Lagrange multipliers or penalty parameters yet.

Make sure you set the Lagrange multipliers before you use this...

Parameters

function

Lagrangian function.

AugLagrangianFunction() [2/2]

AugLagrangianFunction	(	LagrangianFunction &	function,
		const arma::vec &	lambda,
		const double	sigma
	)

Initialize the AugLagrangianFunction with the given LagrangianFunction, Lagrange multipliers, and initial penalty parameter.

Parameters

function	Lagrangian function.
lambda	Initial Lagrange multipliers.
sigma	Initial penalty parameter.

Member Function Documentation

Evaluate() [1/3]

double Evaluate

(

const arma::mat &

coordinates

)

const

Evaluate the objective function of the Augmented Lagrangian function, which is the standard Lagrangian function evaluation plus a penalty term, which penalizes unsatisfied constraints.

Parameters

coordinates

Coordinates to evaluate function at.

Returns

Objective function.

Evaluate() [2/3]

double Evaluate ( const arma::mat &  coordinates ) const

inline

Evaluate() [3/3]

double Evaluate ( const arma::mat &  coordinates ) const

inline

Function() [1/2]

const LagrangianFunction& Function ( ) const

inline

Get the Lagrangian function.

Definition at line 98 of file aug_lagrangian_function.hpp.

Function() [2/2]

LagrangianFunction& Function ( )

inline

Modify the Lagrangian function.

Definition at line 100 of file aug_lagrangian_function.hpp.

GetInitialPoint()

const arma::mat& GetInitialPoint

(

)

const

Get the initial point of the optimization (supplied by the LagrangianFunction).

Returns

Initial point.

Gradient() [1/3]

void Gradient	(	const arma::mat &	coordinates,
		arma::mat &	gradient
	)		const

Evaluate the gradient of the Augmented Lagrangian function.

Parameters

coordinates	Coordinates to evaluate gradient at.
gradient	Matrix to store gradient into.

Gradient() [2/3]

void Gradient ( const arma::mat &  coordinates, arma::mat &  gradient  ) const

inline

Gradient() [3/3]

void Gradient ( const arma::mat &  coordinates, arma::mat &  gradient  ) const

inline

Lambda() [1/2]

const arma::vec& Lambda ( ) const

inline

Get the Lagrange multipliers.

Definition at line 88 of file aug_lagrangian_function.hpp.

Lambda() [2/2]

arma::vec& Lambda ( )

inline

Modify the Lagrange multipliers.

Definition at line 90 of file aug_lagrangian_function.hpp.

Sigma() [1/2]

double Sigma ( ) const

inline

Get sigma (the penalty parameter).

Definition at line 93 of file aug_lagrangian_function.hpp.

Sigma() [2/2]

double& Sigma ( )

inline

Modify sigma (the penalty parameter).

Definition at line 95 of file aug_lagrangian_function.hpp.

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The documentation for this class was generated from the following file:

• src/mlpack/core/optimizers/aug_lagrangian/aug_lagrangian_function.hpp