mlpack::optimization::LovaszThetaSDP Class Reference

This function is the Lovasz-Theta semidefinite program, as implemented in the following paper:. More...

List of all members.

Public Member Functions
	LovaszThetaSDP (const arma::mat &edges)
	Initialize the Lovasz-Theta SDP with the given set of edges.
	LovaszThetaSDP ()
arma::mat &	Edges ()
const arma::mat &	Edges () const
double	Evaluate (const arma::mat &coordinates)
double	EvaluateConstraint (const size_t index, const arma::mat &coordinates)
const arma::mat &	GetInitialPoint ()
void	Gradient (const arma::mat &coordinates, arma::mat &gradient)
void	GradientConstraint (const size_t index, const arma::mat &coordinates, arma::mat &gradient)
size_t	NumConstraints () const
Private Attributes
arma::mat	edges
arma::mat	initialPoint
size_t	vertices

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Detailed Description

This function is the Lovasz-Theta semidefinite program, as implemented in the following paper:.

S. Burer, R. Monteiro "A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization." Journal of Mathematical Programming, 2004

Given a simple, undirected graph G = (V, E), the Lovasz-Theta SDP is defined by:

min_X{Tr(-(e e^T)^T X) : Tr(X) = 1, X_ij = 0 for all (i, j) in E, X >= 0}

where e is the vector of all ones and X has dimension |V| x |V|.

In the Monteiro-Burer formulation, we take X = R * R^T, where R is the coordinates given to the Evaluate(), Gradient(), EvaluateConstraint(), and GradientConstraint() functions.

Definition at line 115 of file aug_lagrangian_test_functions.hpp.

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Constructor & Destructor Documentation

mlpack::optimization::LovaszThetaSDP::LovaszThetaSDP

(

)

mlpack::optimization::LovaszThetaSDP::LovaszThetaSDP

(

const arma::mat &

edges

)

Initialize the Lovasz-Theta SDP with the given set of edges.

The edge matrix should consist of rows of two dimensions, where dimension 0 is the first vertex of the edge and dimension 1 is the second edge (or vice versa, as it doesn't make a difference).

Parameters:

edges

Matrix of edges.

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Member Function Documentation

arma::mat& mlpack::optimization::LovaszThetaSDP::Edges

(

)

[inline]

Definition at line 143 of file aug_lagrangian_test_functions.hpp.

const arma::mat& mlpack::optimization::LovaszThetaSDP::Edges

(

)

const [inline]

Definition at line 142 of file aug_lagrangian_test_functions.hpp.

double mlpack::optimization::LovaszThetaSDP::Evaluate

(

const arma::mat &

coordinates

)

double mlpack::optimization::LovaszThetaSDP::EvaluateConstraint	(	const size_t	index,
		const arma::mat &	coordinates
	)

const arma::mat& mlpack::optimization::LovaszThetaSDP::GetInitialPoint

(

)

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

void mlpack::optimization::LovaszThetaSDP::GradientConstraint	(	const size_t	index,
		const arma::mat &	coordinates,
		arma::mat &	gradient
	)

size_t mlpack::optimization::LovaszThetaSDP::NumConstraints

(

)

const

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Member Data Documentation

arma::mat mlpack::optimization::LovaszThetaSDP::edges [private]

Definition at line 146 of file aug_lagrangian_test_functions.hpp.

arma::mat mlpack::optimization::LovaszThetaSDP::initialPoint [private]

Definition at line 149 of file aug_lagrangian_test_functions.hpp.

size_t mlpack::optimization::LovaszThetaSDP::vertices [private]

Definition at line 147 of file aug_lagrangian_test_functions.hpp.

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

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