NAME¶

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.

SYNOPSIS¶

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.

Detailed Description¶

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: Definition at line 48 of file aug_lagrangian_function.hpp.

Constructor & Destructor Documentation¶

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

template<typename LagrangianFunction> mlpack::optimization::AugLagrangianFunction< LagrangianFunction >:: AugLagrangianFunction (LagrangianFunction &function, const arma::vec &lambda, const doublesigma)¶

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

Member Function Documentation¶

template<typename LagrangianFunction> double mlpack::optimization::AugLagrangianFunction< 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: Returns:

template<typename LagrangianFunction> const LagrangianFunction& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Function () const [inline]¶

Get the Lagrangian function. Definition at line 108 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> LagrangianFunction& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Function () [inline]¶

Modify the Lagrangian function. Definition at line 110 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> const arma::mat& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::GetInitialPoint () const¶

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

template<typename LagrangianFunction> void mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Gradient (const arma::mat &coordinates, arma::mat &gradient) const¶

Evaluate the gradient of the Augmented Lagrangian function. Parameters:

template<typename LagrangianFunction> const arma::vec& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Lambda () const [inline]¶

Get the Lagrange multipliers. Definition at line 98 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> arma::vec& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Lambda () [inline]¶

Modify the Lagrange multipliers. Definition at line 100 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> double mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Sigma () const [inline]¶

Get sigma (the penalty parameter). Definition at line 103 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> double& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::Sigma () [inline]¶

Modify sigma (the penalty parameter). Definition at line 105 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> std::string mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::ToString () const¶

Member Data Documentation¶

template<typename LagrangianFunction> LagrangianFunction& mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::function [private]¶

Instantiation of the function to be optimized. Definition at line 117 of file aug_lagrangian_function.hpp.

template<typename LagrangianFunction> arma::vec mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::lambda [private]¶

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 mlpack::optimization::AugLagrangianFunction< LagrangianFunction >::sigma [private]¶

The penalty parameter. Definition at line 122 of file aug_lagrangian_function.hpp. Referenced by mlpack::optimization::AugLagrangianFunction< mlpack::optimization::LRSDPFunction >::Sigma().

Author¶

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