mlpack
2.2.5
|
The AugLagrangian class implements the Augmented Lagrangian method of optimization. More...
Public Types | |
typedef L_BFGS < AugLagrangianFunction < LagrangianFunction > > | L_BFGSType |
Shorthand for the type of the L-BFGS optimizer we'll be using. More... | |
Public Member Functions | |
AugLagrangian (LagrangianFunction &function) | |
Initialize the Augmented Lagrangian with the default L-BFGS optimizer. More... | |
AugLagrangian (AugLagrangianFunction< LagrangianFunction > &augfunc, L_BFGSType &lbfgs) | |
Initialize the Augmented Lagrangian with a custom L-BFGS optimizer. More... | |
const LagrangianFunction & | Function () const |
Get the LagrangianFunction. More... | |
LagrangianFunction & | Function () |
Modify the LagrangianFunction. More... | |
const arma::vec & | Lambda () const |
Get the Lagrange multipliers. More... | |
arma::vec & | Lambda () |
Modify the Lagrange multipliers (i.e. set them before optimization). More... | |
const L_BFGSType & | LBFGS () const |
Get the L-BFGS object used for the actual optimization. More... | |
L_BFGSType & | LBFGS () |
Modify the L-BFGS object used for the actual optimization. More... | |
bool | Optimize (arma::mat &coordinates, const size_t maxIterations=1000) |
Optimize the function. More... | |
bool | Optimize (arma::mat &coordinates, const arma::vec &initLambda, const double initSigma, const size_t maxIterations=1000) |
Optimize the function, giving initial estimates for the Lagrange multipliers. More... | |
double | Sigma () const |
Get the penalty parameter. More... | |
double & | Sigma () |
Modify the penalty parameter. More... | |
The AugLagrangian 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".
The template class LagrangianFunction must implement the following five methods:
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.
LagrangianFunction | Function which can be optimized by this class. |
Definition at line 49 of file aug_lagrangian.hpp.
typedef L_BFGS<AugLagrangianFunction<LagrangianFunction> > L_BFGSType |
Shorthand for the type of the L-BFGS optimizer we'll be using.
Definition at line 54 of file aug_lagrangian.hpp.
AugLagrangian | ( | LagrangianFunction & | function | ) |
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.
function | The function to be optimized. |
AugLagrangian | ( | AugLagrangianFunction< LagrangianFunction > & | augfunc, |
L_BFGSType & | lbfgs | ||
) |
Initialize the Augmented Lagrangian with a custom L-BFGS optimizer.
function | The function to be optimized. This must be a pre-created utility AugLagrangianFunction. |
lbfgs | The custom L-BFGS optimizer to be used. This should have already been initialized with the given AugLagrangianFunction. |
|
inline |
Get the LagrangianFunction.
Definition at line 107 of file aug_lagrangian.hpp.
|
inline |
Modify the LagrangianFunction.
Definition at line 109 of file aug_lagrangian.hpp.
|
inline |
Get the Lagrange multipliers.
Definition at line 117 of file aug_lagrangian.hpp.
|
inline |
Modify the Lagrange multipliers (i.e. set them before optimization).
Definition at line 119 of file aug_lagrangian.hpp.
|
inline |
Get the L-BFGS object used for the actual optimization.
Definition at line 112 of file aug_lagrangian.hpp.
|
inline |
Modify the L-BFGS object used for the actual optimization.
Definition at line 114 of file aug_lagrangian.hpp.
bool Optimize | ( | arma::mat & | coordinates, |
const size_t | maxIterations = 1000 |
||
) |
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 Optimize().
coordinates | Output matrix to store the optimized coordinates in. |
maxIterations | Maximum number of iterations of the Augmented Lagrangian algorithm. 0 indicates no maximum. |
sigma | Initial penalty parameter. |
bool Optimize | ( | arma::mat & | coordinates, |
const arma::vec & | initLambda, | ||
const double | initSigma, | ||
const size_t | maxIterations = 1000 |
||
) |
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).
coordinates | Output matrix to store the optimized coordinates in. |
initLambda | Vector of initial Lagrange multipliers. Should have length equal to the number of constraints. |
initSigma | Initial penalty parameter. |
maxIterations | Maximum number of iterations of the Augmented Lagrangian algorithm. 0 indicates no maximum. |
|
inline |
Get the penalty parameter.
Definition at line 122 of file aug_lagrangian.hpp.
|
inline |
Modify the penalty parameter.
Definition at line 124 of file aug_lagrangian.hpp.