mlpack_optimization_AugLagrangianFunction (3)

Public Member Functions

AugLagrangianFunction (LagrangianFunction &function)

Initialize the AugLagrangianFunction, but don't set the Lagrange multipliers or penalty parameters yet. AugLagrangianFunction (LagrangianFunction &function, const arma::vec &lambda, const double sigma)

Initialize the AugLagrangianFunction with the given LagrangianFunction, Lagrange multipliers, and initial penalty parameter. double Evaluate (const arma::mat &coordinates) const

Evaluate the objective function of the Augmented Lagrangian function, which is the standard Lagrangian function evaluation plus a penalty term, which penalizes unsatisfied constraints. const LagrangianFunction & Function () const

Get the Lagrangian function. LagrangianFunction & Function ()

Modify the Lagrangian function. const arma::mat & GetInitialPoint () const

Get the initial point of the optimization (supplied by the LagrangianFunction). void Gradient (const arma::mat &coordinates, arma::mat &gradient) const

Evaluate the gradient of the Augmented Lagrangian function. const arma::vec & Lambda () const

Get the Lagrange multipliers. arma::vec & Lambda ()

Modify the Lagrange multipliers. double Sigma () const

Get sigma (the penalty parameter). double & Sigma ()

Modify sigma (the penalty parameter). std::string ToString () const

Private Attributes

LagrangianFunction & function

Instantiation of the function to be optimized. arma::vec lambda

The Lagrange multipliers. double sigma

The penalty parameter.

template<typename LagrangianFunction>class mlpack::optimization::AugLagrangianFunction< LagrangianFunction >

This is a utility class used by AugLagrangian, meant to wrap a LagrangianFunction into a function usable by a simple optimizer like L-BFGS.

Given a LagrangianFunction which follows the format outlined in the documentation for AugLagrangian, this class provides Evaluate(), Gradient(), and GetInitialPoint() functions which allow this class to be used with a simple optimizer like L-BFGS.

This class can be specialized for your particular implementation -- commonly, a faster method for computing the overall objective and gradient of the augmented Lagrangian function can be implemented than the naive, default implementation given. Use class template specialization and re-implement all of the methods (unfortunately, C++ specialization rules mean you have to re-implement everything).

Template Parameters:

LagrangianFunction Lagrangian function to be used.

Definition at line 48 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::\fBAugLagrangianFunction\fP (LagrangianFunction &function)

Initialize the AugLagrangianFunction, but don't set the Lagrange multipliers or penalty parameters yet. Make sure you set the Lagrange multipliers before you use this...

Parameters:

function Lagrangian function.

template<typename LagrangianFunction> \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::\fBAugLagrangianFunction\fP (LagrangianFunction &function, const arma::vec &lambda, const doublesigma)

Initialize the AugLagrangianFunction with the given LagrangianFunction, Lagrange multipliers, and initial penalty parameter.

Parameters:

function Lagrangian function.

lambda Initial Lagrange multipliers.

sigma Initial penalty parameter.

template<typename LagrangianFunction> double \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::Evaluate (const arma::mat &coordinates) const

Evaluate the objective function of the Augmented Lagrangian function, which is the standard Lagrangian function evaluation plus a penalty term, which penalizes unsatisfied constraints.

Parameters:

coordinates Coordinates to evaluate function at.

Returns:

Objective function.

template<typename LagrangianFunction> const LagrangianFunction& \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::Function () const\fC [inline]\fP

Get the Lagrangian function.

Definition at line 108 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> LagrangianFunction& \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::Function ()\fC [inline]\fP

Modify the Lagrangian function.

Definition at line 110 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> const arma::mat& \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::GetInitialPoint () const

Get the initial point of the optimization (supplied by the LagrangianFunction).

Returns:

Initial point.

template<typename LagrangianFunction> void \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::Gradient (const arma::mat &coordinates, arma::mat &gradient) const

Evaluate the gradient of the Augmented Lagrangian function.

Parameters:

coordinates Coordinates to evaluate gradient at.

gradient Matrix to store gradient into.

template<typename LagrangianFunction> const arma::vec& \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::Lambda () const\fC [inline]\fP

Get the Lagrange multipliers.

Definition at line 98 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> arma::vec& \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::Lambda ()\fC [inline]\fP

Modify the Lagrange multipliers.

Definition at line 100 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> double \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::Sigma () const\fC [inline]\fP

Get sigma (the penalty parameter).

Definition at line 103 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> double& \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::Sigma ()\fC [inline]\fP

Modify sigma (the penalty parameter).

Definition at line 105 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> std::string \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::ToString () const

template<typename LagrangianFunction> LagrangianFunction& \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::function\fC [private]\fP

Instantiation of the function to be optimized.

Definition at line 117 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> arma::vec \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::lambda\fC [private]\fP

The Lagrange multipliers.

Definition at line 120 of file aug_lagrangian_function.hpp.

Referenced by mlpack::optimization::AugLagrangianFunction< mlpack::optimization::LRSDPFunction >::Lambda().

template<typename LagrangianFunction> double \fBmlpack::optimization::AugLagrangianFunction\fP< LagrangianFunction >::sigma\fC [private]\fP

The penalty parameter.

Definition at line 122 of file aug_lagrangian_function.hpp.

Referenced by mlpack::optimization::AugLagrangianFunction< mlpack::optimization::LRSDPFunction >::Sigma().

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