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This is a utility class used by AugLagrangian, meant to wrap a LagrangianFunction into a function usable by a simple optimizer like L-BFGS. More...
Public Member Functions | |
AugLagrangianFunction (LagrangianFunction &function) | |
Initialize the AugLagrangianFunction, but don't set the Lagrange multipliers or penalty parameters yet. More... | |
AugLagrangianFunction (LagrangianFunction &function, const arma::vec &lambda, const double sigma) | |
Initialize the AugLagrangianFunction with the given LagrangianFunction, Lagrange multipliers, and initial penalty parameter. More... | |
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. More... | |
template < > | |
double | Evaluate (const arma::mat &coordinates) const |
template < > | |
double | Evaluate (const arma::mat &coordinates) const |
const LagrangianFunction & | Function () const |
Get the Lagrangian function. More... | |
LagrangianFunction & | Function () |
Modify the Lagrangian function. More... | |
const arma::mat & | GetInitialPoint () const |
Get the initial point of the optimization (supplied by the LagrangianFunction). More... | |
void | Gradient (const arma::mat &coordinates, arma::mat &gradient) const |
Evaluate the gradient of the Augmented Lagrangian function. More... | |
template < > | |
void | Gradient (const arma::mat &coordinates, arma::mat &gradient) const |
template < > | |
void | Gradient (const arma::mat &coordinates, arma::mat &gradient) const |
const arma::vec & | Lambda () const |
Get the Lagrange multipliers. More... | |
arma::vec & | Lambda () |
Modify the Lagrange multipliers. More... | |
double | Sigma () const |
Get sigma (the penalty parameter). More... | |
double & | Sigma () |
Modify sigma (the penalty parameter). More... | |
Detailed Description
template<typenameLagrangianFunction>
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 38 of file aug_lagrangian_function.hpp.
Constructor & Destructor Documentation
◆ AugLagrangianFunction() [1/2]
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
-
function Lagrangian function.
◆ AugLagrangianFunction() [2/2]
AugLagrangianFunction | ( | LagrangianFunction & | function, |
const arma::vec & | lambda, | ||
const double | sigma | ||
) |
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.
Member Function Documentation
◆ Evaluate() [1/3]
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.
- Parameters
-
coordinates Coordinates to evaluate function at.
- Returns
- Objective function.
◆ Evaluate() [2/3]
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inline |
◆ Evaluate() [3/3]
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inline |
◆ Function() [1/2]
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inline |
Get the Lagrangian function.
Definition at line 98 of file aug_lagrangian_function.hpp.
◆ Function() [2/2]
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inline |
Modify the Lagrangian function.
Definition at line 100 of file aug_lagrangian_function.hpp.
◆ GetInitialPoint()
const arma::mat& GetInitialPoint | ( | ) | const |
Get the initial point of the optimization (supplied by the LagrangianFunction).
- Returns
- Initial point.
◆ Gradient() [1/3]
void 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.
◆ Gradient() [2/3]
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inline |
◆ Gradient() [3/3]
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inline |
◆ Lambda() [1/2]
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inline |
Get the Lagrange multipliers.
Definition at line 88 of file aug_lagrangian_function.hpp.
◆ Lambda() [2/2]
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inline |
Modify the Lagrange multipliers.
Definition at line 90 of file aug_lagrangian_function.hpp.
◆ Sigma() [1/2]
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inline |
Get sigma (the penalty parameter).
Definition at line 93 of file aug_lagrangian_function.hpp.
◆ Sigma() [2/2]
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inline |
Modify sigma (the penalty parameter).
Definition at line 95 of file aug_lagrangian_function.hpp.
The documentation for this class was generated from the following file:
- src/mlpack/core/optimizers/aug_lagrangian/aug_lagrangian_function.hpp
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