.TH "mlpack::optimization::AugLagrangian< LagrangianFunction >" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::optimization::AugLagrangian< LagrangianFunction > \- 
.PP
The \fBAugLagrangian\fP class implements the Augmented Lagrangian method of optimization\&.  

.SH SYNOPSIS
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.PP
.SS "Public Types"

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.RI "typedef \fBL_BFGS\fP
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< \fBAugLagrangianFunction\fP
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< LagrangianFunction > > \fBL_BFGSType\fP"
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.RI "\fIShorthand for the type of the L-BFGS optimizer we'll be using\&. \fP"
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.SS "Public Member Functions"

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.RI "\fBAugLagrangian\fP (LagrangianFunction &\fBfunction\fP)"
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.RI "\fIInitialize the Augmented Lagrangian with the default L-BFGS optimizer\&. \fP"
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.RI "\fBAugLagrangian\fP (\fBAugLagrangianFunction\fP< LagrangianFunction > &\fBaugfunc\fP, \fBL_BFGSType\fP &\fBlbfgs\fP)"
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.RI "\fIInitialize the Augmented Lagrangian with a custom L-BFGS optimizer\&. \fP"
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.RI "const LagrangianFunction & \fBFunction\fP () const "
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.RI "\fIGet the LagrangianFunction\&. \fP"
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.RI "LagrangianFunction & \fBFunction\fP ()"
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.RI "\fIModify the LagrangianFunction\&. \fP"
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.RI "const arma::vec & \fBLambda\fP () const "
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.RI "\fIGet the Lagrange multipliers\&. \fP"
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.RI "arma::vec & \fBLambda\fP ()"
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.RI "\fIModify the Lagrange multipliers (i\&.e\&. set them before optimization)\&. \fP"
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.RI "const \fBL_BFGSType\fP & \fBLBFGS\fP () const "
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.RI "\fIGet the L-BFGS object used for the actual optimization\&. \fP"
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.RI "\fBL_BFGSType\fP & \fBLBFGS\fP ()"
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.RI "\fIModify the L-BFGS object used for the actual optimization\&. \fP"
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.RI "bool \fBOptimize\fP (arma::mat &coordinates, const size_t maxIterations=1000)"
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.RI "\fIOptimize the function\&. \fP"
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.RI "bool \fBOptimize\fP (arma::mat &coordinates, const arma::vec &initLambda, const double initSigma, const size_t maxIterations=1000)"
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.RI "\fIOptimize the function, giving initial estimates for the Lagrange multipliers\&. \fP"
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.RI "double \fBSigma\fP () const "
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.RI "\fIGet the penalty parameter\&. \fP"
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.RI "double & \fBSigma\fP ()"
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.RI "\fIModify the penalty parameter\&. \fP"
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.RI "std::string \fBToString\fP () const "
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.SS "Private Attributes"

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.RI "\fBAugLagrangianFunction\fP
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< LagrangianFunction > \fBaugfunc\fP"
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.RI "\fIInternally used \fBAugLagrangianFunction\fP which holds the function we are optimizing\&. \fP"
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.RI "LagrangianFunction & \fBfunction\fP"
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.RI "\fIFunction to be optimized\&. \fP"
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.RI "\fBL_BFGSType\fP & \fBlbfgs\fP"
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.RI "\fIThe L-BFGS optimizer that we will use\&. \fP"
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.RI "\fBL_BFGSType\fP \fBlbfgsInternal\fP"
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.RI "\fIIf the user did not pass an \fBL_BFGS\fP object, we'll use our own internal one\&. \fP"
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.SH "Detailed Description"
.PP 

.SS "template<typename LagrangianFunction>class mlpack::optimization::AugLagrangian< LagrangianFunction >"
The \fBAugLagrangian\fP class implements the Augmented Lagrangian method of optimization\&. 

In this scheme, a penalty term is added to the Lagrangian\&. This method is also called the 'method of multipliers'\&.
.PP
The template class LagrangianFunction must implement the following five methods:
.PP
.IP "\(bu" 2
double Evaluate(const arma::mat& coordinates);
.IP "\(bu" 2
void Gradient(const arma::mat& coordinates, arma::mat& gradient);
.IP "\(bu" 2
size_t NumConstraints();
.IP "\(bu" 2
double EvaluateConstraint(size_t index, const arma::mat& coordinates);
.IP "\(bu" 2
double GradientConstraint(size_t index, const arma::mat& coordinates, arma::mat& gradient);
.PP
.PP
The number of constraints must be greater than or equal to 0, and EvaluateConstraint() should evaluate the constraint at the given index for the given coordinates\&. Evaluate() should provide the objective function value for the given coordinates\&.
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\fBTemplate Parameters:\fP
.RS 4
\fILagrangianFunction\fP Function which can be optimized by this class\&. 
.RE
.PP

.PP
Definition at line 59 of file aug_lagrangian\&.hpp\&.
.SH "Member Typedef Documentation"
.PP 
.SS "template<typename LagrangianFunction> typedef \fBL_BFGS\fP<\fBAugLagrangianFunction\fP<LagrangianFunction> > \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::\fBL_BFGSType\fP"

.PP
Shorthand for the type of the L-BFGS optimizer we'll be using\&. 
.PP
Definition at line 64 of file aug_lagrangian\&.hpp\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "template<typename LagrangianFunction> \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::\fBAugLagrangian\fP (LagrangianFunction &function)"

.PP
Initialize the Augmented Lagrangian with the default L-BFGS optimizer\&. We limit the number of L-BFGS iterations to 1000, rather than the unlimited default L-BFGS\&.
.PP
\fBParameters:\fP
.RS 4
\fIfunction\fP The function to be optimized\&. 
.RE
.PP

.SS "template<typename LagrangianFunction> \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::\fBAugLagrangian\fP (\fBAugLagrangianFunction\fP< LagrangianFunction > &augfunc, \fBL_BFGSType\fP &lbfgs)"

.PP
Initialize the Augmented Lagrangian with a custom L-BFGS optimizer\&. 
.PP
\fBParameters:\fP
.RS 4
\fIfunction\fP The function to be optimized\&. This must be a pre-created utility \fBAugLagrangianFunction\fP\&. 
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\fIlbfgs\fP The custom L-BFGS optimizer to be used\&. This should have already been initialized with the given \fBAugLagrangianFunction\fP\&. 
.RE
.PP

.SH "Member Function Documentation"
.PP 
.SS "template<typename LagrangianFunction> const LagrangianFunction& \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::Function () const\fC [inline]\fP"

.PP
Get the LagrangianFunction\&. 
.PP
Definition at line 117 of file aug_lagrangian\&.hpp\&.
.SS "template<typename LagrangianFunction> LagrangianFunction& \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::Function ()\fC [inline]\fP"

.PP
Modify the LagrangianFunction\&. 
.PP
Definition at line 119 of file aug_lagrangian\&.hpp\&.
.SS "template<typename LagrangianFunction> const arma::vec& \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::Lambda () const\fC [inline]\fP"

.PP
Get the Lagrange multipliers\&. 
.PP
Definition at line 127 of file aug_lagrangian\&.hpp\&.
.SS "template<typename LagrangianFunction> arma::vec& \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::Lambda ()\fC [inline]\fP"

.PP
Modify the Lagrange multipliers (i\&.e\&. set them before optimization)\&. 
.PP
Definition at line 129 of file aug_lagrangian\&.hpp\&.
.SS "template<typename LagrangianFunction> const \fBL_BFGSType\fP& \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::LBFGS () const\fC [inline]\fP"

.PP
Get the L-BFGS object used for the actual optimization\&. 
.PP
Definition at line 122 of file aug_lagrangian\&.hpp\&.
.SS "template<typename LagrangianFunction> \fBL_BFGSType\fP& \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::LBFGS ()\fC [inline]\fP"

.PP
Modify the L-BFGS object used for the actual optimization\&. 
.PP
Definition at line 124 of file aug_lagrangian\&.hpp\&.
.SS "template<typename LagrangianFunction> bool \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::Optimize (arma::mat &coordinates, const size_tmaxIterations = \fC1000\fP)"

.PP
Optimize the function\&. The value '1' is used for the initial value of each Lagrange multiplier\&. To set the Lagrange multipliers yourself, use the other overload of \fBOptimize()\fP\&.
.PP
\fBParameters:\fP
.RS 4
\fIcoordinates\fP Output matrix to store the optimized coordinates in\&. 
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\fImaxIterations\fP Maximum number of iterations of the Augmented Lagrangian algorithm\&. 0 indicates no maximum\&. 
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\fIsigma\fP Initial penalty parameter\&. 
.RE
.PP

.SS "template<typename LagrangianFunction> bool \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::Optimize (arma::mat &coordinates, const arma::vec &initLambda, const doubleinitSigma, const size_tmaxIterations = \fC1000\fP)"

.PP
Optimize the function, giving initial estimates for the Lagrange multipliers\&. The vector of Lagrange multipliers will be modified to contain the Lagrange multipliers of the final solution (if one is found)\&.
.PP
\fBParameters:\fP
.RS 4
\fIcoordinates\fP Output matrix to store the optimized coordinates in\&. 
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\fIinitLambda\fP Vector of initial Lagrange multipliers\&. Should have length equal to the number of constraints\&. 
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\fIinitSigma\fP Initial penalty parameter\&. 
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\fImaxIterations\fP Maximum number of iterations of the Augmented Lagrangian algorithm\&. 0 indicates no maximum\&. 
.RE
.PP

.SS "template<typename LagrangianFunction> double \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::Sigma () const\fC [inline]\fP"

.PP
Get the penalty parameter\&. 
.PP
Definition at line 132 of file aug_lagrangian\&.hpp\&.
.SS "template<typename LagrangianFunction> double& \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::Sigma ()\fC [inline]\fP"

.PP
Modify the penalty parameter\&. 
.PP
Definition at line 134 of file aug_lagrangian\&.hpp\&.
.SS "template<typename LagrangianFunction> std::string \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::ToString () const"

.SH "Member Data Documentation"
.PP 
.SS "template<typename LagrangianFunction> \fBAugLagrangianFunction\fP<LagrangianFunction> \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::augfunc\fC [private]\fP"

.PP
Internally used \fBAugLagrangianFunction\fP which holds the function we are optimizing\&. This isn't publically accessible, but we provide ways to get to the Lagrange multipliers and the penalty parameter sigma\&. 
.PP
Definition at line 146 of file aug_lagrangian\&.hpp\&.
.PP
Referenced by mlpack::optimization::AugLagrangian< mlpack::optimization::LRSDPFunction >::Lambda(), and mlpack::optimization::AugLagrangian< mlpack::optimization::LRSDPFunction >::Sigma()\&.
.SS "template<typename LagrangianFunction> LagrangianFunction& \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::function\fC [private]\fP"

.PP
Function to be optimized\&. 
.PP
Definition at line 141 of file aug_lagrangian\&.hpp\&.
.SS "template<typename LagrangianFunction> \fBL_BFGSType\fP& \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::lbfgs\fC [private]\fP"

.PP
The L-BFGS optimizer that we will use\&. 
.PP
Definition at line 152 of file aug_lagrangian\&.hpp\&.
.PP
Referenced by mlpack::optimization::AugLagrangian< mlpack::optimization::LRSDPFunction >::LBFGS()\&.
.SS "template<typename LagrangianFunction> \fBL_BFGSType\fP \fBmlpack::optimization::AugLagrangian\fP< LagrangianFunction >::lbfgsInternal\fC [private]\fP"

.PP
If the user did not pass an \fBL_BFGS\fP object, we'll use our own internal one\&. 
.PP
Definition at line 149 of file aug_lagrangian\&.hpp\&.

.SH "Author"
.PP 
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