LRSDP< SDPType > Class Template Reference

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

Inheritance diagram for LRSDP< SDPType >:

Public Member Functions
	LRSDP (const size_t numSparseConstraints, const size_t numDenseConstraints, const arma::mat &initialPoint, const size_t maxIterations=1000)
	Create an LRSDP to be optimized. More...
const AugLagrangian &	AugLag () const
	Return the augmented Lagrangian object. More...
AugLagrangian &	AugLag ()
	Modify the augmented Lagrangian object. More...
const LRSDPFunction< SDPType > &	Function () const
	Return the function to be optimized. More...
LRSDPFunction< SDPType > &	Function ()
	Modify the function to be optimized. More...
size_t	MaxIterations () const
	Get the maximum number of iterations. More...
size_t &	MaxIterations ()
	Modify the maximum number of iterations. More...
double	Optimize (arma::mat &coordinates)
	Create an LRSDP object with the given SDP problem to be solved, and the given initial point. More...
const SDPType &	SDP () const
	Return the SDP that will be solved. More...
SDPType &	SDP ()
	Modify the SDP that will be solved. More...

Detailed Description

template

<

typename

SDPType

>

class mlpack::optimization::LRSDP< SDPType >

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 30 of file lrsdp.hpp.

Constructor & Destructor Documentation

LRSDP()

LRSDP	(	const size_t	numSparseConstraints,
		const size_t	numDenseConstraints,
		const arma::mat &	initialPoint,
		const size_t	maxIterations = 1000
	)

Create an LRSDP to be optimized.

The solution will end up being a matrix of size (rows) x (rank). To construct each constraint and the objective function, use the function SDP() in order to access the SDPType object associated with this optimizer.

Parameters

numSparseConstraints	Number of sparse constraints in the problem.
numDenseConstraints	Number of dense constraints in the problem.
initialPoint	Initial point of the optimization.
maxIterations	Maximum number of iterations.

Member Function Documentation

AugLag() [1/2]

const AugLagrangian& AugLag ( ) const

inline

Return the augmented Lagrangian object.

Definition at line 84 of file lrsdp.hpp.

AugLag() [2/2]

AugLagrangian& AugLag ( )

inline

Modify the augmented Lagrangian object.

Definition at line 86 of file lrsdp.hpp.

Function() [1/2]

const LRSDPFunction<SDPType>& Function ( ) const

inline

Return the function to be optimized.

Definition at line 79 of file lrsdp.hpp.

Function() [2/2]

LRSDPFunction<SDPType>& Function ( )

inline

Modify the function to be optimized.

Definition at line 81 of file lrsdp.hpp.

MaxIterations() [1/2]

size_t MaxIterations ( ) const

inline

Get the maximum number of iterations.

Definition at line 89 of file lrsdp.hpp.

MaxIterations() [2/2]

size_t& MaxIterations ( )

inline

Modify the maximum number of iterations.

Definition at line 91 of file lrsdp.hpp.

Optimize()

double Optimize

(

arma::mat &

coordinates

)

Create an LRSDP object with the given SDP problem to be solved, and the given initial point.

Note that the SDP may be modified later by calling SDP() to access the object.

TODO: this is currently not implemented.

Parameters

sdp	SDP to be solved.
initialPoint	Initial point of the optimization.
maxIterations	Maximum number of iterations.

LRSDP(const SDPType& sdp, const arma::mat& initialPoint, const size_t maxIterations = 1000); 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.

SDP() [1/2]

const SDPType& SDP ( ) const

inline

Return the SDP that will be solved.

Definition at line 74 of file lrsdp.hpp.

SDP() [2/2]

SDPType& SDP ( )

inline

Modify the SDP that will be solved.

Definition at line 76 of file lrsdp.hpp.

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

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