.TH "mlpack::optimization::LovaszThetaSDP" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::optimization::LovaszThetaSDP \- 
.PP
This function is the Lovasz-Theta semidefinite program, as implemented in the following paper:  

.SH SYNOPSIS
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.PP
.SS "Public Member Functions"

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.RI "\fBLovaszThetaSDP\fP ()"
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.RI "\fBLovaszThetaSDP\fP (const arma::mat &\fBedges\fP)"
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.RI "\fIInitialize the Lovasz-Theta SDP with the given set of edges\&. \fP"
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.RI "const arma::mat & \fBEdges\fP () const "
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.RI "arma::mat & \fBEdges\fP ()"
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.RI "double \fBEvaluate\fP (const arma::mat &coordinates)"
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.RI "double \fBEvaluateConstraint\fP (const size_t index, const arma::mat &coordinates)"
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.RI "const arma::mat & \fBGetInitialPoint\fP ()"
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.RI "void \fBGradient\fP (const arma::mat &coordinates, arma::mat &gradient)"
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.RI "void \fBGradientConstraint\fP (const size_t index, const arma::mat &coordinates, arma::mat &gradient)"
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.RI "size_t \fBNumConstraints\fP () const "
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.SS "Private Attributes"

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.RI "arma::mat \fBedges\fP"
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.RI "arma::mat \fBinitialPoint\fP"
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.RI "size_t \fBvertices\fP"
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.SH "Detailed Description"
.PP 
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
.PP
Given a simple, undirected graph G = (V, E), the Lovasz-Theta SDP is defined by:
.PP
min_X{Tr(-(e e^T)^T X) : Tr(X) = 1, X_ij = 0 for all (i, j) in E, X >= 0}
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where e is the vector of all ones and X has dimension |V| x |V|\&.
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In the Monteiro-Burer formulation, we take X = R * R^T, where R is the coordinates given to the \fBEvaluate()\fP, \fBGradient()\fP, \fBEvaluateConstraint()\fP, and \fBGradientConstraint()\fP functions\&. 
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Definition at line 118 of file aug_lagrangian_test_functions\&.hpp\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "mlpack::optimization::LovaszThetaSDP::LovaszThetaSDP ()"

.SS "mlpack::optimization::LovaszThetaSDP::LovaszThetaSDP (const arma::mat &edges)"

.PP
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)\&.
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\fBParameters:\fP
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\fIedges\fP Matrix of edges\&. 
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.SH "Member Function Documentation"
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.SS "const arma::mat& mlpack::optimization::LovaszThetaSDP::Edges () const\fC [inline]\fP"

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Definition at line 145 of file aug_lagrangian_test_functions\&.hpp\&.
.PP
References edges\&.
.SS "arma::mat& mlpack::optimization::LovaszThetaSDP::Edges ()\fC [inline]\fP"

.PP
Definition at line 146 of file aug_lagrangian_test_functions\&.hpp\&.
.PP
References edges\&.
.SS "double mlpack::optimization::LovaszThetaSDP::Evaluate (const arma::mat &coordinates)"

.SS "double mlpack::optimization::LovaszThetaSDP::EvaluateConstraint (const size_tindex, const arma::mat &coordinates)"

.SS "const arma::mat& mlpack::optimization::LovaszThetaSDP::GetInitialPoint ()"

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

.SS "void mlpack::optimization::LovaszThetaSDP::GradientConstraint (const size_tindex, const arma::mat &coordinates, arma::mat &gradient)"

.SS "size_t mlpack::optimization::LovaszThetaSDP::NumConstraints () const"

.SH "Member Data Documentation"
.PP 
.SS "arma::mat mlpack::optimization::LovaszThetaSDP::edges\fC [private]\fP"

.PP
Definition at line 149 of file aug_lagrangian_test_functions\&.hpp\&.
.PP
Referenced by Edges()\&.
.SS "arma::mat mlpack::optimization::LovaszThetaSDP::initialPoint\fC [private]\fP"

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Definition at line 152 of file aug_lagrangian_test_functions\&.hpp\&.
.SS "size_t mlpack::optimization::LovaszThetaSDP::vertices\fC [private]\fP"

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Definition at line 150 of file aug_lagrangian_test_functions\&.hpp\&.

.SH "Author"
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Generated automatically by Doxygen for MLPACK from the source code\&.