SYNOPSIS

Public Member Functions

LovaszThetaSDP ()

LovaszThetaSDP (const arma::mat &edges)
Initialize the Lovasz-Theta SDP with the given set of edges.
const arma::mat & Edges () const

arma::mat & Edges ()

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

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 118 of file aug_lagrangian_test_functions.hpp.

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.

Member Function Documentation

const arma::mat& mlpack::optimization::LovaszThetaSDP::Edges () const [inline]

Definition at line 145 of file aug_lagrangian_test_functions.hpp.

References edges.

arma::mat& mlpack::optimization::LovaszThetaSDP::Edges () [inline]

Definition at line 146 of file aug_lagrangian_test_functions.hpp.

References edges.

double mlpack::optimization::LovaszThetaSDP::Evaluate (const arma::mat &coordinates)

double mlpack::optimization::LovaszThetaSDP::EvaluateConstraint (const size_tindex, 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_tindex, const arma::mat &coordinates, arma::mat &gradient)

size_t mlpack::optimization::LovaszThetaSDP::NumConstraints () const

Member Data Documentation

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

Definition at line 149 of file aug_lagrangian_test_functions.hpp.

Referenced by Edges().

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

Definition at line 152 of file aug_lagrangian_test_functions.hpp.

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

Definition at line 150 of file aug_lagrangian_test_functions.hpp.

Author

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