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...

Inheritance diagram for mlpack::optimization::AugLagrangianFunction< LagrangianFunction >:

[legend]

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...

Private Attributes
LagrangianFunction &	function
	Instantiation of the function to be optimized. More...

arma::vec	lambda
	The Lagrange multipliers. More...

double	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

template<typename LagrangianFunction>

mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::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.

template<typename LagrangianFunction>

mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::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

template<typename LagrangianFunction>

double mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::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.

template<>

double mlpack::optimization::AugLagrangianFunction< LRSDPFunction< SDP< arma::sp_mat > > >::Evaluate ( const arma::mat & coordinates ) const

inline

template<>

double mlpack::optimization::AugLagrangianFunction< LRSDPFunction< SDP< arma::mat > > >::Evaluate ( const arma::mat & coordinates ) const

inline

template<typename LagrangianFunction>

const LagrangianFunction& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Function ( ) const

inline

Get the Lagrangian function.

Definition at line 98 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction>

LagrangianFunction& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Function ( )

inline

Modify the Lagrangian function.

Definition at line 100 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction>

const arma::mat& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::GetInitialPoint ( ) const

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

Returns: Initial point.

template<typename LagrangianFunction>

void mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::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.

template<>

void mlpack::optimization::AugLagrangianFunction< LRSDPFunction< SDP< arma::sp_mat > > >::Gradient	(	const arma::mat &	coordinates,
		arma::mat &	gradient
	)		const

inline

template<>

void mlpack::optimization::AugLagrangianFunction< LRSDPFunction< SDP< arma::mat > > >::Gradient	(	const arma::mat &	coordinates,
		arma::mat &	gradient
	)		const

inline

template<typename LagrangianFunction>

const arma::vec& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Lambda ( ) const

inline

Get the Lagrange multipliers.

Definition at line 88 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction>

arma::vec& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Lambda ( )

inline

Modify the Lagrange multipliers.

Definition at line 90 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction>

double mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Sigma ( ) const

inline

Get sigma (the penalty parameter).

Definition at line 93 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction>

double& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Sigma ( )

inline

Modify sigma (the penalty parameter).

Definition at line 95 of file aug_lagrangian_function.hpp.

Member Data Documentation

template<typename LagrangianFunction>

LagrangianFunction& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::function

private

Instantiation of the function to be optimized.

Definition at line 104 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction>

arma::vec mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::lambda

private

The Lagrange multipliers.

Definition at line 107 of file aug_lagrangian_function.hpp.

Referenced by mlpack::optimization::AugLagrangianFunction< mlpack::optimization::LRSDPFunction< optimization::SDP< arma::sp_mat > > >::Lambda().

template<typename LagrangianFunction>

double mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::sigma

private

The penalty parameter.

Definition at line 109 of file aug_lagrangian_function.hpp.

Referenced by mlpack::optimization::AugLagrangianFunction< mlpack::optimization::LRSDPFunction< optimization::SDP< arma::sp_mat > > >::Sigma().

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

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

Public Member Functions

Private Attributes

Detailed Description

template<typename LagrangianFunction> class mlpack::optimization::AugLagrangianFunction< LagrangianFunction >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename LagrangianFunction>
class mlpack::optimization::AugLagrangianFunction< LagrangianFunction >