LRSDP is the implementation of Monteiro and Burer's formulation of low-rank semidefinite programs (LR-SDP). More...

Collaboration diagram for mlpack::optimization::LRSDP:

Public Member Functions
	LRSDP (const size_t numConstraints, const arma::mat &initialPoint)
	Create an LRSDP to be optimized. More...

	LRSDP (const size_t numConstraints, const arma::mat &initialPoint, AugLagrangian< LRSDPFunction > &augLagrangian)
	Create an LRSDP to be optimized, passing in an already-created AugLagrangian object. More...

const std::vector< arma::mat > &	A () const
	Return the vector of A matrices (which correspond to the constraints). More...

std::vector< arma::mat > &	A ()
	Modify the veector of A matrices (which correspond to the constraints). More...

const arma::uvec &	AModes () const
	Return the vector of modes for the A matrices. More...

arma::uvec &	AModes ()
	Modify the vector of modes for the A matrices. More...

const AugLagrangian < LRSDPFunction > &	AugLag () const
	Return the augmented Lagrangian object. More...

AugLagrangian< LRSDPFunction > &	AugLag ()
	Modify the augmented Lagrangian object. More...

const arma::vec &	B () const
	Return the vector of B values. More...

arma::vec &	B ()
	Modify the vector of B values. More...

const arma::mat &	C () const
	Return the objective function matrix (C). More...

arma::mat &	C ()
	Modify the objective function matrix (C). More...

const LRSDPFunction &	Function () const
	Return the function to be optimized. More...

LRSDPFunction &	Function ()
	Modify the function to be optimized. More...

double	Optimize (arma::mat &coordinates)
	Optimize the LRSDP and return the final objective value. More...

std::string	ToString () const
	Return a string representation of the object. More...

Private Attributes
AugLagrangian< LRSDPFunction >	augLag
	The AugLagrangian object which will be used for optimization. More...

LRSDPFunction	function
	Function to optimize, which the AugLagrangian object holds. More...

Detailed Description

LRSDP is the implementation of Monteiro and Burer's formulation of low-rank semidefinite programs (LR-SDP).

This solver uses the augmented Lagrangian optimizer to solve low-rank semidefinite programs.

Definition at line 39 of file lrsdp.hpp.

Constructor & Destructor Documentation

mlpack::optimization::LRSDP::LRSDP	(	const size_t	numConstraints,
		const arma::mat &	initialPoint
	)

Create an LRSDP to be optimized.

The solution will end up being a matrix of size (rank) x (rows). To construct each constraint and the objective function, use the functions A(), B(), and C() to set them correctly.

Parameters

numConstraints	Number of constraints in the problem.
rank	Rank of the solution (<= rows).
rows	Number of rows in the solution.

mlpack::optimization::LRSDP::LRSDP	(	const size_t	numConstraints,
		const arma::mat &	initialPoint,
		AugLagrangian< LRSDPFunction > &	augLagrangian
	)

Create an LRSDP to be optimized, passing in an already-created AugLagrangian object.

The given initial point should be set to the size (rows) x (rank), where (rank) is the reduced rank of the problem.

Parameters

numConstraints	Number of constraints in the problem.
initialPoint	Initial point of the optimization.
auglag	Pre-initialized AugLagrangian<LRSDP> object.

Member Function Documentation

const std::vector<arma::mat>& mlpack::optimization::LRSDP::A ( ) const

inline

Return the vector of A matrices (which correspond to the constraints).

Definition at line 81 of file lrsdp.hpp.

std::vector<arma::mat>& mlpack::optimization::LRSDP::A ( )

inline

Modify the veector of A matrices (which correspond to the constraints).

Definition at line 83 of file lrsdp.hpp.

const arma::uvec& mlpack::optimization::LRSDP::AModes ( ) const

inline

Return the vector of modes for the A matrices.

Definition at line 86 of file lrsdp.hpp.

arma::uvec& mlpack::optimization::LRSDP::AModes ( )

inline

Modify the vector of modes for the A matrices.

Definition at line 88 of file lrsdp.hpp.

const AugLagrangian<LRSDPFunction>& mlpack::optimization::LRSDP::AugLag ( ) const

inline

Return the augmented Lagrangian object.

Definition at line 101 of file lrsdp.hpp.

References augLag.

AugLagrangian<LRSDPFunction>& mlpack::optimization::LRSDP::AugLag ( )

inline

Modify the augmented Lagrangian object.

Definition at line 103 of file lrsdp.hpp.

References augLag.

const arma::vec& mlpack::optimization::LRSDP::B ( ) const

inline

Return the vector of B values.

Definition at line 91 of file lrsdp.hpp.

arma::vec& mlpack::optimization::LRSDP::B ( )

inline

Modify the vector of B values.

Definition at line 93 of file lrsdp.hpp.

const arma::mat& mlpack::optimization::LRSDP::C ( ) const

inline

Return the objective function matrix (C).

Definition at line 76 of file lrsdp.hpp.

arma::mat& mlpack::optimization::LRSDP::C ( )

inline

Modify the objective function matrix (C).

Definition at line 78 of file lrsdp.hpp.

const LRSDPFunction& mlpack::optimization::LRSDP::Function ( ) const

inline

Return the function to be optimized.

Definition at line 96 of file lrsdp.hpp.

LRSDPFunction& mlpack::optimization::LRSDP::Function ( )

inline

Modify the function to be optimized.

Definition at line 98 of file lrsdp.hpp.

double mlpack::optimization::LRSDP::Optimize ( arma::mat & coordinates )

Optimize the LRSDP and return the final objective value.

The given coordinates will be modified to contain the final solution.

Parameters

coordinates Starting coordinates for the optimization.

std::string mlpack::optimization::LRSDP::ToString ( ) const

Return a string representation of the object.

Member Data Documentation

AugLagrangian<LRSDPFunction> mlpack::optimization::LRSDP::augLag

private

The AugLagrangian object which will be used for optimization.

Definition at line 113 of file lrsdp.hpp.

Referenced by AugLag().

LRSDPFunction mlpack::optimization::LRSDP::function

private

Function to optimize, which the AugLagrangian object holds.

Definition at line 110 of file lrsdp.hpp.

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

src/mlpack/core/optimizers/lrsdp/lrsdp.hpp

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation