The AugLagrangian class implements the Augmented Lagrangian method of optimization. More...

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

Public Types
typedef L_BFGS< AugLagrangianFunction< LagrangianFunction > >	L_BFGSType
	Shorthand for the type of the L-BFGS optimizer we'll be using. More...

Public Member Functions
	AugLagrangian (LagrangianFunction &function)
	Initialize the Augmented Lagrangian with the default L-BFGS optimizer. More...

	AugLagrangian (AugLagrangianFunction< LagrangianFunction > &augfunc, L_BFGSType &lbfgs)
	Initialize the Augmented Lagrangian with a custom L-BFGS optimizer. More...

const LagrangianFunction &	Function () const
	Get the LagrangianFunction. More...

LagrangianFunction &	Function ()
	Modify the LagrangianFunction. More...

const arma::vec &	Lambda () const
	Get the Lagrange multipliers. More...

arma::vec &	Lambda ()
	Modify the Lagrange multipliers (i.e. set them before optimization). More...

const L_BFGSType &	LBFGS () const
	Get the L-BFGS object used for the actual optimization. More...

L_BFGSType &	LBFGS ()
	Modify the L-BFGS object used for the actual optimization. More...

bool	Optimize (arma::mat &coordinates, const size_t maxIterations=1000)
	Optimize the function. More...

bool	Optimize (arma::mat &coordinates, const arma::vec &initLambda, const double initSigma, const size_t maxIterations=1000)
	Optimize the function, giving initial estimates for the Lagrange multipliers. More...

double	Sigma () const
	Get the penalty parameter. More...

double &	Sigma ()
	Modify the penalty parameter. More...

Private Attributes
AugLagrangianFunction< LagrangianFunction >	augfunc
	Internally used AugLagrangianFunction which holds the function we are optimizing. More...

LagrangianFunction &	function
	Function to be optimized. More...

L_BFGSType &	lbfgs
	The L-BFGS optimizer that we will use. More...

L_BFGSType	lbfgsInternal
	If the user did not pass an L_BFGS object, we'll use our own internal one. More...

Detailed Description

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

The AugLagrangian class implements the Augmented Lagrangian method of optimization.

In this scheme, a penalty term is added to the Lagrangian. This method is also called the "method of multipliers".

The template class LagrangianFunction must implement the following five methods:

double Evaluate(const arma::mat& coordinates);
void Gradient(const arma::mat& coordinates, arma::mat& gradient);
size_t NumConstraints();
double EvaluateConstraint(size_t index, const arma::mat& coordinates);
double GradientConstraint(size_t index, const arma::mat& coordinates, arma::mat& gradient);

The number of constraints must be greater than or equal to 0, and EvaluateConstraint() should evaluate the constraint at the given index for the given coordinates. Evaluate() should provide the objective function value for the given coordinates.

Template Parameters

LagrangianFunction Function which can be optimized by this class.

Definition at line 49 of file aug_lagrangian.hpp.

Member Typedef Documentation

template<typename LagrangianFunction>

typedef L_BFGS<AugLagrangianFunction<LagrangianFunction> > mlpack::optimization::AugLagrangian< LagrangianFunction >::L_BFGSType

Shorthand for the type of the L-BFGS optimizer we'll be using.

Definition at line 54 of file aug_lagrangian.hpp.

Constructor & Destructor Documentation

template<typename LagrangianFunction>

mlpack::optimization::AugLagrangian< LagrangianFunction >::AugLagrangian ( LagrangianFunction & function )

Initialize the Augmented Lagrangian with the default L-BFGS optimizer.

We limit the number of L-BFGS iterations to 1000, rather than the unlimited default L-BFGS.

Parameters

function The function to be optimized.

template<typename LagrangianFunction>

mlpack::optimization::AugLagrangian< LagrangianFunction >::AugLagrangian	(	AugLagrangianFunction< LagrangianFunction > &	augfunc,
		L_BFGSType &	lbfgs
	)

Initialize the Augmented Lagrangian with a custom L-BFGS optimizer.

Parameters

function	The function to be optimized. This must be a pre-created utility AugLagrangianFunction.
lbfgs	The custom L-BFGS optimizer to be used. This should have already been initialized with the given AugLagrangianFunction.

Member Function Documentation

template<typename LagrangianFunction>

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

inline

Get the LagrangianFunction.

Definition at line 107 of file aug_lagrangian.hpp.

template<typename LagrangianFunction>

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

inline

Modify the LagrangianFunction.

Definition at line 109 of file aug_lagrangian.hpp.

template<typename LagrangianFunction>

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

inline

Get the Lagrange multipliers.

Definition at line 117 of file aug_lagrangian.hpp.

template<typename LagrangianFunction>

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

inline

Modify the Lagrange multipliers (i.e. set them before optimization).

Definition at line 119 of file aug_lagrangian.hpp.

template<typename LagrangianFunction>

const L_BFGSType& mlpack::optimization::AugLagrangian< LagrangianFunction >::LBFGS ( ) const

inline

Get the L-BFGS object used for the actual optimization.

Definition at line 112 of file aug_lagrangian.hpp.

template<typename LagrangianFunction>

L_BFGSType& mlpack::optimization::AugLagrangian< LagrangianFunction >::LBFGS ( )

inline

Modify the L-BFGS object used for the actual optimization.

Definition at line 114 of file aug_lagrangian.hpp.

template<typename LagrangianFunction>

bool mlpack::optimization::AugLagrangian< LagrangianFunction >::Optimize	(	arma::mat &	coordinates,
		const size_t	maxIterations = `1000`
	)

Optimize the function.

The value '1' is used for the initial value of each Lagrange multiplier. To set the Lagrange multipliers yourself, use the other overload of Optimize().

Parameters

coordinates	Output matrix to store the optimized coordinates in.
maxIterations	Maximum number of iterations of the Augmented Lagrangian algorithm. 0 indicates no maximum.
sigma	Initial penalty parameter.

template<typename LagrangianFunction>

bool mlpack::optimization::AugLagrangian< LagrangianFunction >::Optimize	(	arma::mat &	coordinates,
		const arma::vec &	initLambda,
		const double	initSigma,
		const size_t	maxIterations = `1000`
	)

Optimize the function, giving initial estimates for the Lagrange multipliers.

The vector of Lagrange multipliers will be modified to contain the Lagrange multipliers of the final solution (if one is found).

Parameters

coordinates	Output matrix to store the optimized coordinates in.
initLambda	Vector of initial Lagrange multipliers. Should have length equal to the number of constraints.
initSigma	Initial penalty parameter.
maxIterations	Maximum number of iterations of the Augmented Lagrangian algorithm. 0 indicates no maximum.

template<typename LagrangianFunction>

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

inline

Get the penalty parameter.

Definition at line 122 of file aug_lagrangian.hpp.

template<typename LagrangianFunction>

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

inline

Modify the penalty parameter.

Definition at line 124 of file aug_lagrangian.hpp.

Member Data Documentation

template<typename LagrangianFunction>

AugLagrangianFunction<LagrangianFunction> mlpack::optimization::AugLagrangian< LagrangianFunction >::augfunc

private

Internally used AugLagrangianFunction which holds the function we are optimizing.

This isn't publically accessible, but we provide ways to get to the Lagrange multipliers and the penalty parameter sigma.

Definition at line 133 of file aug_lagrangian.hpp.

Referenced by mlpack::optimization::AugLagrangian< mlpack::optimization::LRSDPFunction< optimization::SDP< arma::sp_mat > > >::Lambda(), and mlpack::optimization::AugLagrangian< mlpack::optimization::LRSDPFunction< optimization::SDP< arma::sp_mat > > >::Sigma().

template<typename LagrangianFunction>

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

private

Function to be optimized.

Definition at line 128 of file aug_lagrangian.hpp.

template<typename LagrangianFunction>

L_BFGSType& mlpack::optimization::AugLagrangian< LagrangianFunction >::lbfgs

private

The L-BFGS optimizer that we will use.

Definition at line 139 of file aug_lagrangian.hpp.

Referenced by mlpack::optimization::AugLagrangian< mlpack::optimization::LRSDPFunction< optimization::SDP< arma::sp_mat > > >::LBFGS().

template<typename LagrangianFunction>

L_BFGSType mlpack::optimization::AugLagrangian< LagrangianFunction >::lbfgsInternal

private

If the user did not pass an L_BFGS object, we'll use our own internal one.

Definition at line 136 of file aug_lagrangian.hpp.

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

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

Public Types

Public Member Functions

Private Attributes

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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