BFGS optimizations. More...

Classes
struct	DebugProblem
	Debug wrapper for any problem. More...

struct	NoOutput
	NoOutput struct. More...

struct	OptimizationParameters
	Parameters for limited step length BFGS algorithm. More...

struct	OptimizationResult
	The optimization result. More...

struct	OstreamOutput
	Class for the output to an `std::ostream`. More...

struct	scalar_traits
	Traits for scalar values. More...

struct	scalar_traits< double >
	Scalar for `double` values. More...

Typedefs
template<typename Scalar >
using	Vector = Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >
	Vector type used. More...

template<typename Scalar >
using	Matrix = Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic >
	Matrix type used. More...

template<typename Scalar >
using	DiagonalMatrix = Eigen::DiagonalMatrix< Scalar, Eigen::Dynamic, Eigen::Dynamic >
	Diagonal matrix type used. More...

Enumerations
enum	Linesearch { Linesearch::Backtracking }
	Line search algorithm. More...

enum	Alpha0Policy { Constant, Alpha0Policy::ConstantScaling, Alpha0Policy::Interpolation }
	Selection of initial step length alpha0. More...

enum	Status : int { GeneralFailure = -256, Status::InvalidMaximumValue = -129, Status::LineSearchFailed = -128, Status::LineSearchMinimum = -127, Status::LineSearchMaxIterations = -126, Status::WrongSearchDirection = -125, Status::InvalidBounds = -124, Status::Converged = 0, Status::Success = 0, Status::MaxIterations = 1, Status::MinChange = 2, Status::MinusInfinity = 3, Status::MinValue = 4, Status::XGradChange = 5, Status::Running = 256 }
	Status of the optimizer. More...

enum	OutputLevel { Nothing, OutputLevel::Error, OutputLevel::Warning, OutputLevel::Status, OutputLevel::Debug }
	The output level for filtering. More...

Functions
template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	lsl_bfgs (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform a BFGS optimization with identification of the maximum step length (LSL-BFGS). More...

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	bfgs (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform a BFGS optimization without identification of the maximum step length (BFGS). More...

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	lsl_bfgs_b (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform a BFGS optimization with box constraints and identification of the maximum step length (LSL-BFGS-B). More...

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	bfgs_b (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform a BFGS optimization with box constraints and without identification of the maximum step length (BFGS-B). More...

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	lsl_gd (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform a gradient descent optimization with identification of the maximum step length. More...

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	gd (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform a gradient descent optimization without identification of the maximum step length. More...

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	lsl_lbfgs (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform an L-BFGS optimization with identification of the maximum step length (LSL-L-BFGS). More...

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	lbfgs (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform an L-BFGS optimization without identification of the maximum step length (L-BFGS). More...

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	lsl_lbfgs_b (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform an L-BFGS optimization with box constraints and identification of the maximum step length (LSL-L-BFGS-B). More...

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>
OptimizationResult< Scalar >	lbfgs_b (Problem &problem, const Vector< Scalar > &x0, const OptimizationParameters< Scalar > &params, OutputFunction &output_function=OutputFunction())
	Perform an L-BFGS optimization with box constraints and without identification of the maximum step length (L-BFGS-B). More...

template<typename Scalar >
OptimizationParameters< Scalar >	getOptimizationParameters ()
	Get optimization parameters for this type. More...

template<>
OptimizationParameters< double >	getOptimizationParameters< double > ()
	Default optimization parameters for `double`.

std::ostream &	operator<< (std::ostream &os, const Status &status)
	Output of Status on `std::ostream`. More...

std::ostream &	operator<< (std::ostream &os, const OutputLevel &level)
	Output operator for textual level output. More...

template<typename OutputFunction >
bool	is_output_enabled (OutputFunction &output_function, OutputLevel curr_level, decltype(output_function.output_level) *=nullptr)

bool	is_output_enabled (...)
	Catch-all function.

Detailed Description

BFGS optimizations.

L-BFGS-B optimizations.

L-BFGS optimizations.

Gradient descent optimizations.

BFGS-B optimizations.

This file contains functions for the optimization using the BFGS algorithm with and without the limitation of step lengths.

Warning: These functions are not suited for large-scale optimization.

This file contains functions for the optimization with box constraints using the BFGS-B algorithm with and without the limitation of step lengths.

Warning: These functions are not suited for large-scale optimization.

This file contains functions for the optimization using the gradient descent algorithm with and without the limitation of step lengths.

Warning: These functions are used for comparison only, the various BFGS implementations are usually far superior.

This file contains functions for the optimization using the L-BFGS algorithm with and without the limitation of step lengths.

This file contains functions for the optimization using the L-BFGS-B algorithm with and without the limitation of step lengths.

Typedef Documentation

◆ DiagonalMatrix

template<typename Scalar >

using LSLOpt::DiagonalMatrix = typedef Eigen::DiagonalMatrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>

Diagonal matrix type used.

Template Parameters

Scalar The scalar type of the coefficients.

This is a diagonal matrix (an Eigen::DiagonalMatrix).

◆ Matrix

template<typename Scalar >

using LSLOpt::Matrix = typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>

Matrix type used.

Template Parameters

Scalar The scalar type of the coefficients.

This is a matrix (an Eigen::Matrix).

◆ Vector

template<typename Scalar >

using LSLOpt::Vector = typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1>

Vector type used.

Template Parameters

Scalar The scalar type of the coefficients.

This is a column vector (an Eigen::Matrix).

Enumeration Type Documentation

◆ Alpha0Policy

enum LSLOpt::Alpha0Policy

strong

Selection of initial step length alpha0.

Enumerator
ConstantScaling	use max alpha from algorithm (or 1.0)
Interpolation	scale old alpha by phi'_{k-1}(0) / phi'_{k}(0)

◆ Linesearch

enum LSLOpt::Linesearch

strong

Line search algorithm.

Enumerator
Backtracking	Armijo backtracking.

◆ OutputLevel

enum LSLOpt::OutputLevel

strong

The output level for filtering.

Enumerator
Error	not output
Warning	show fatal errors
Status	show warnings
Debug	show status messages

◆ Status

enum LSLOpt::Status : int

strong

Status of the optimizer.

Non-negative values indicate success or regular termination.

Negative values indicate failures.

Enumerator
InvalidMaximumValue	general failure
LineSearchFailed	no valid max alpha obtained
LineSearchMinimum	general line search failure
LineSearchMaxIterations	step length too small
WrongSearchDirection	maximum number of line search iterations reached
InvalidBounds	optimizer going uphill, probably wrong gradient!
Converged	the bounds are invalid
Success	optimization converged
MaxIterations	optimization successful, the same as `Converged`
MinChange	maximum number of iterations reached
MinusInfinity	objective function doesn't change anymore
MinValue	function reached minus infinity
XGradChange	function value reached stopping value
Running	the gradient or the parameters don't change anymore

Function Documentation

◆ bfgs()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::bfgs	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform a BFGS optimization without identification of the maximum step length (BFGS).

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a BFGS minimization of the given objective function. Internally, it uses an backtracking line search and uses a damped update strategy to ensure the positive definiteness of the Hessian approximation (and it's inverse).

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point as well as the maximum allowed step length at a given point and a given direction:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

Warning: This is a BFGS implementation (NOT L-BFGS) and therefore not suited for large optimization problems.

Note: This is a convenience function to perform a standard BFGS without maximum step length identification.

◆ bfgs_b()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::bfgs_b	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform a BFGS optimization with box constraints and without identification of the maximum step length (BFGS-B).

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a BFGS minimization of the given objective function. Internally, it uses an backtracking line search and uses a damped update strategy to ensure the positive definiteness of the Hessian approximation (and it's inverse).

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point as well as the maximum allowed step length at a given point and a given direction and the upper and lower bounds on the parameters:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

const Vector<Scalar>& lower_bounds();

const Vector<Scalar>& upper_bounds();

Warning: This is a BFGS implementation (NOT L-BFGS) and therefore not suited for large optimization problems.

Note: This is a convenience function to perform a standard BFGS-B without maximum step length identification.

Byrd, R.H., Lu, P., Nocedal, J., Zhu, C. A Limited Memory Algorithm for Bound Constrained Optimization.

SIAM Journal of Scientific and Statistical Computing. 16(5). 1190-1208.

◆ gd()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::gd	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform a gradient descent optimization without identification of the maximum step length.

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a gradient descent minimization of the given objective function.

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point as well as the maximum allowed step length at a given point and a given direction:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

Note: This is a convenience function to perform a standard gradient descent without maximum step length identification.

◆ getOptimizationParameters()

template<typename Scalar >

OptimizationParameters<Scalar> LSLOpt::getOptimizationParameters ( )

Get optimization parameters for this type.

Template Parameters

Scalar Type of scalar values.

◆ is_output_enabled()

template<typename OutputFunction >

bool LSLOpt::is_output_enabled	(	OutputFunction &	output_function,
		OutputLevel	curr_level,
		decltype(output_function.output_level) *	= `nullptr`
	)

Check if the output function is activated at this level. This uses SFINAE, i.e. if the output_function does not provide the output_level attribute, this function is not used.

Parameters

output_function	The output function.
curr_level	Current leve of message.

◆ lbfgs()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::lbfgs	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform an L-BFGS optimization without identification of the maximum step length (L-BFGS).

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a L-BFGS minimization of the given objective function. Internally, it uses an backtracking line search and uses a damped update strategy to ensure the positive definiteness of the Hessian approximation (and it's inverse).

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point as well as the maximum allowed step length at a given point and a given direction:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

Note: This is a L-BFGS implementation and therefore suited for large optimization problems.; This is a convenience function to perform a standard L-BFGS without maximum step length identification.

◆ lbfgs_b()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::lbfgs_b	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform an L-BFGS optimization with box constraints and without identification of the maximum step length (L-BFGS-B).

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a L-BFGS-B minimization of the given objective function. Internally, it uses an backtracking line search and uses a damped update strategy to ensure the positive definiteness of the Hessian approximation (and it's inverse).

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point as well as the maximum allowed step length at a given point and a given direction and the upper and lower bounds on the parameters:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

const Vector<Scalar>& lower_bounds();

const Vector<Scalar>& upper_bounds();

Note: This is a L-BFGS-B implementation and therefore suited for large optimization problems.; This is a convenience function to perform a standard L-BFGS-B without maximum step length identification.

Byrd, R.H., Lu, P., Nocedal, J., Zhu, C. A Limited Memory Algorithm for Bound Constrained Optimization.

SIAM Journal of Scientific and Statistical Computing. 16(5). 1190-1208.

Morales, J.L, Nocedal, J. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization.

ACM Transactions on Mathematical Software. 38(1). 7:1-7:4.

◆ lsl_bfgs()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::lsl_bfgs	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform a BFGS optimization with identification of the maximum step length (LSL-BFGS).

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a BFGS minimization of the given objective function. Internally, it uses an backtracking line search and uses a damped update strategy to ensure the positive definiteness of the Hessian approximation (and it's inverse).

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point, the initially allowed step length at a given point and a given direction as well as a function checking if a change from one point to the other is acceptable:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

Scalar initial_step_length(const Vector<Scalar>& x, const Vector<Scalar>& p);

Scalar change_acceptable(const Vector<Scalar>& x, const Vector<Scalar>& xp); (should return a value <= 0.0 if the change is acceptable, > 0.0 otherwise).

Warning: This is a BFGS implementation (NOT L-BFGS) and therefore not suited for large optimization problems.

◆ lsl_bfgs_b()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::lsl_bfgs_b	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform a BFGS optimization with box constraints and identification of the maximum step length (LSL-BFGS-B).

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a BFGS-B minimization of the given objective function. Internally, it uses an backtracking line search and uses a damped update strategy to ensure the positive definiteness of the Hessian approximation (and it's inverse).

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point, the initially allowed step length at a given point and a given direction as well as a function checking if a change from one point to the other is acceptable and the upper and lower bounds on the parameters:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

Scalar initial_step_length(const Vector<Scalar>& x, const Vector<Scalar>& p);

Scalar change_acceptable(const Vector<Scalar>& x, const Vector<Scalar>& xp); (should return a value <= 0.0 if the change is acceptable, > 0.0 otherwise).

const Vector<Scalar>& lower_bounds();

const Vector<Scalar>& upper_bounds();

Warning: This is a BFGS-B implementation (NOT L-BFGS) and therefore not suited for large optimization problems.

Byrd, R.H., Lu, P., Nocedal, J., Zhu, C. A Limited Memory Algorithm for Bound Constrained Optimization.

SIAM Journal of Scientific and Statistical Computing. 16(5). 1190-1208.

◆ lsl_gd()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::lsl_gd	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform a gradient descent optimization with identification of the maximum step length.

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a gradient descent minimization of the given objective function.

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point, the initially allowed step length at a given point and a given direction as well as a function checking if a change from one point to the other is acceptable:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

double initial_step_length(const Eigen::VectorXd& x, const Eigen::VectorXd& p);

bool is_change_acceptable(const Eigen::VectorXd& x, const Eigen::VectorXd& xp);

◆ lsl_lbfgs()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::lsl_lbfgs	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform an L-BFGS optimization with identification of the maximum step length (LSL-L-BFGS).

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a L-BFGS minimization of the given objective function. Internally, it uses an backtracking line search and uses a damped update strategy to ensure the positive definiteness of the Hessian approximation (and it's inverse).

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point, the initially allowed step length at a given point and a given direction as well as a function checking if a change from one point to the other is acceptable:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

Scalar initial_step_length(const Vector<Scalar>& x, const Vector<Scalar>& p);

Scalar change_acceptable(const Vector<Scalar>& x, const Vector<Scalar>& xp); (should return a value <= 0.0 if the change is acceptable, > 0.0 otherwise).

Note: This is a L-BFGS implementation and therefore suited for large optimization problems.

◆ lsl_lbfgs_b()

template<typename Problem , typename Scalar , typename OutputFunction = NoOutput>

OptimizationResult<Scalar> LSLOpt::lsl_lbfgs_b	(	Problem &	problem,
		const Vector< Scalar > &	x0,
		const OptimizationParameters< Scalar > &	params,
		OutputFunction &	output_function = `OutputFunction()`
	)

Perform an L-BFGS optimization with box constraints and identification of the maximum step length (LSL-L-BFGS-B).

Parameters

problem	Objective function to minimize.
x0	Starting point for optimization.
params	BFGS parameters.
output_function	Function for output of status and error messages.

This performs a L-BFGS-B minimization of the given objective function. Internally, it uses an backtracking line search and uses a damped update strategy to ensure the positive definiteness of the Hessian approximation (and it's inverse).

The problem must provide the following functions, calculating the value at a given point, the gradient at a given point, the initially allowed step length at a given point and a given direction as well as a function checking if a change from one point to the other is acceptable and the upper and lower bounds on the parameters:

Scalar value(const Vector<Scalar>& x);

Vector<Scalar> gradient(const Vector<Scalar>& x);

Scalar initial_step_length(const Vector<Scalar>& x, const Vector<Scalar>& p);

Scalar change_acceptable(const Vector<Scalar>& x, const Vector<Scalar>& xp); (should return a value <= 0.0 if the change is acceptable, > 0.0 otherwise).

const Vector<Scalar>& lower_bounds();

const Vector<Scalar>& upper_bounds();

Note: This is a L-BFGS-B implementation and therefore suited for large optimization problems.

Byrd, R.H., Lu, P., Nocedal, J., Zhu, C. A Limited Memory Algorithm for Bound Constrained Optimization.

SIAM Journal of Scientific and Statistical Computing. 16(5). 1190-1208.

Morales, J.L, Nocedal, J. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization.

ACM Transactions on Mathematical Software. 38(1). 7:1-7:4.

◆ operator<<() [1/2]

std::ostream& LSLOpt::operator<<	(	std::ostream &	os,
		const OutputLevel &	level
	)

inline

Output operator for textual level output.

Parameters

os	Output stream.
level	The output leve.

Returns: The output stream.

◆ operator<<() [2/2]

std::ostream& LSLOpt::operator<<	(	std::ostream &	os,
		const Status &	status
	)

inline

Output of Status on std::ostream.

Parameters

os	Output stream.
status	Status to output.

Returns: The output stream os.

Classes

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

◆ DiagonalMatrix

◆ Matrix

◆ Vector

Enumeration Type Documentation

◆ Alpha0Policy

◆ Linesearch

◆ OutputLevel

◆ Status

Function Documentation

◆ bfgs()

◆ bfgs_b()

◆ gd()

◆ getOptimizationParameters()

◆ is_output_enabled()

◆ lbfgs()

◆ lbfgs_b()

◆ lsl_bfgs()

◆ lsl_bfgs_b()

◆ lsl_gd()

◆ lsl_lbfgs()

◆ lsl_lbfgs_b()

◆ operator<<() [1/2]

◆ operator<<() [2/2]