Class container for the Nelder-Mead's method. More...

#include <NelderMead.hh>

Inherits Optimist::Optimizer::Optimizer< Real, N, NelderMead< Real, N > >.

Public Types
using	Simplex = std::vector<Vector>
Public Types inherited from Optimist::Optimizer::Optimizer< Real, N, NelderMead< Real, N > >
using	Vector
using	RowVector
using	Matrix
Public Types inherited from Optimist::SolverBase< Real, N, 1, NelderMead< Real, N >, false >
using	InputType
using	OutputType
using	TraceType
using	FirstDerivativeType
using	SecondDerivativeType

Public Member Functions
	NelderMead ()
std::string	name_impl () const
void	initialize (Vector const &x_ini, Real delta)
Vector	centroid () const
template<typename FunctionLambda>
void	sort (FunctionLambda &&function)
Vector	reflection () const
	Computes the reflection point.
Vector	expansion (Vector const &x) const
	Computes the expansion point.
Vector	outward_contraction (Vector const &x) const
Vector	inward_contraction () const
void	shrink ()
bool	solve_impl (FunctionLambda &&function, Vector const &x_ini, Vector &x_sol)
Public Member Functions inherited from Optimist::Optimizer::Optimizer< Real, N, NelderMead< Real, N > >
	Optimizer ()
std::string	name () const
Integer	gradient_evaluations () const
Integer	max_gradient_evaluations () const
Integer	hessian_evaluations () const
Integer	max_hessian_evaluations () const
Public Member Functions inherited from Optimist::SolverBase< Real, N, 1, NelderMead< Real, N >, false >
	SolverBase ()
InputType const &	lower_bound () const
InputType const &	upper_bound () const
void	bounds (InputType const &t_lower_bound, InputType const &t_upper_bound)
constexpr Integer	input_dimension () const
constexpr Integer	output_dimension () const
Integer	function_evaluations () const
void	max_function_evaluations (Integer t_max_function_evaluations)
Integer	iterations () const
Integer	max_iterations () const
Real	alpha () const
Integer	relaxations () const
Integer	max_relaxations () const
Real	tolerance () const
void	verbose_mode (bool t_verbose)
void	enable_verbose_mode ()
void	disable_verbose_mode ()
void	damped_mode (bool t_damped)
void	enable_damped_mode ()
void	disable_damped_mode ()
std::string	task () const
bool	converged () const
const TraceType &	trace () const
std::ostream &	ostream () const
bool	solve (FunctionLambda &&function, InputType const &x_ini, InputType &x_sol)
bool	rootfind (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, InputType const &x_ini, InputType &x_sol)
bool	optimize (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, InputType const &x_ini, InputType &x_sol)
std::string	name () const

Static Public Attributes
static constexpr bool	requires_function {true}
static constexpr bool	requires_first_derivative {false}
static constexpr bool	requires_second_derivative {false}
Static Public Attributes inherited from Optimist::Optimizer::Optimizer< Real, N, NelderMead< Real, N > >
static constexpr bool	is_rootfinder
static constexpr bool	is_optimizer

Private Attributes
Simplex	m_s
Vector	m_c
Real	m_alpha {1.0}
Real	m_gamma {2.0}
Real	m_rho {0.5}
Real	m_sigma {0.5}

Additional Inherited Members
Protected Member Functions inherited from Optimist::Optimizer::Optimizer< Real, N, NelderMead< Real, N > >
bool	evaluate_gradient (GradientLambda &&gradient, Vector const &x, Matrix &out)
bool	evaluate_hessian (HessianLambda &&hessian, Vector const &x, Matrix &out)
bool	solve (FunctionLambda &&function, Vector const &x_ini, Vector &x_sol)
Protected Member Functions inherited from Optimist::SolverBase< Real, N, 1, NelderMead< Real, N >, false >
Integer	first_derivative_evaluations () const
Integer	max_first_derivative_evaluations () const
Integer	second_derivative_evaluations () const
Integer	max_second_derivative_evaluations () const
void	reset ()
bool	evaluate_function (FunctionLambda &&function, InputType const &x, OutputType &out)
bool	evaluate_first_derivative (FirstDerivativeLambda &&function, InputType const &x, FirstDerivativeType &out)
bool	evaluate_second_derivative (SecondDerivativeLambda &&function, InputType const &x, SecondDerivativeType &out)
void	store_trace (InputType const &x)
bool	damp (FunctionLambda &&function, InputType const &x_old, InputType const &function_old, InputType const &step_old, InputType &x_new, InputType &function_new, InputType &step_new)
void	header ()
void	bottom ()
void	info (Real residuals, std::string const &notes="-")
Protected Attributes inherited from Optimist::SolverBase< Real, N, 1, NelderMead< Real, N >, false >
InputType	m_lower_bound
InputType	m_upper_bound
Integer	m_function_evaluations
Integer	m_first_derivative_evaluations
Integer	m_second_derivative_evaluations
Integer	m_max_function_evaluations
Integer	m_max_first_derivative_evaluations
Integer	m_max_second_derivative_evaluations
Integer	m_iterations
Integer	m_max_iterations
Real	m_alpha
Integer	m_relaxations
Integer	m_max_relaxations
Real	m_tolerance
bool	m_verbose
bool	m_damped
std::ostream *	m_ostream
std::string	m_task
bool	m_converged
TraceType	m_trace

Detailed Description

template<typename Real, Integer N>
class Optimist::Optimizer::NelderMead< Real, N >

Template Parameters

Real	Scalar number type.
N	Dimension of the root-finding problem.

Member Typedef Documentation

◆ Simplex

template<typename Real, Integer N>

using Optimist::Optimizer::NelderMead< Real, N >::Simplex = std::vector<Vector>

Constructor & Destructor Documentation

◆ NelderMead()

template<typename Real, Integer N>

Optimist::Optimizer::NelderMead< Real, N >::NelderMead ( )

inline

Nelder-Mead shrink coefficient. Class constructor for the NelderMead solver.

Member Function Documentation

◆ centroid()

template<typename Real, Integer N>

Vector Optimist::Optimizer::NelderMead< Real, N >::centroid ( ) const

inline

Compute the centroid of the simplex.

Returns: The centroid of the simplex.

◆ expansion()

template<typename Real, Integer N>

Vector Optimist::Optimizer::NelderMead< Real, N >::expansion ( Vector const & x ) const

inline

Parameters

[in] x The reflection point.

Returns: The expansion point.

◆ initialize()

template<typename Real, Integer N>

void Optimist::Optimizer::NelderMead< Real, N >::initialize	(	Vector const &	x_ini,
		Real	delta )

inline

Initialize the simplex around a given centroid.

Parameters

[in]	x_ini	The initial point.
[in]	delta	The initial step size.

◆ inward_contraction()

template<typename Real, Integer N>

Vector Optimist::Optimizer::NelderMead< Real, N >::inward_contraction ( ) const

inline

Computes the inward contraction point.

Returns: The contraction point.

◆ name_impl()

template<typename Real, Integer N>

std::string Optimist::Optimizer::NelderMead< Real, N >::name_impl ( ) const

inline

Get the Nelder-Mead's solver name.

Returns: The Nelder-Mead's solver name.

◆ outward_contraction()

template<typename Real, Integer N>

Vector Optimist::Optimizer::NelderMead< Real, N >::outward_contraction ( Vector const & x ) const

inline

Computes the outward contraction point.

Parameters

[in] x The reflection point.

Returns: The contraction point.

◆ reflection()

template<typename Real, Integer N>

Vector Optimist::Optimizer::NelderMead< Real, N >::reflection ( ) const

inline

Returns: The reflection point.

◆ shrink()

template<typename Real, Integer N>

void Optimist::Optimizer::NelderMead< Real, N >::shrink ( )

inline

Shrinks the simplex towards the best point.

◆ solve_impl()

template<typename Real, Integer N>

bool Optimist::Optimizer::NelderMead< Real, N >::solve_impl	(	FunctionLambda &&	function,
		Vector const &	x_ini,
		Vector &	x_sol )

inline

Solve the nonlinear system of equations \( \mathbf{f}(\mathbf{x}) = 0 \), with \(\mathbf{f}: \mathbb{R}^n \rightarrow \mathbb{R}^n \).

Template Parameters

FunctionLambda Function lambda type.

Parameters

[in]	function	Function lambda.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

Returns: The convergence boolean flag.

◆ sort()

template<typename Real, Integer N>

template<typename FunctionLambda>

void Optimist::Optimizer::NelderMead< Real, N >::sort ( FunctionLambda && function )

inline

Sort the points of the simplex based on the function values and updates the centroid.

Template Parameters

FunctionLambda Function lambda type.

Parameters

[in] function Function lambda.

Member Data Documentation

◆ m_alpha

template<typename Real, Integer N>

Real Optimist::Optimizer::NelderMead< Real, N >::m_alpha {1.0}

private

◆ m_c

template<typename Real, Integer N>

Vector Optimist::Optimizer::NelderMead< Real, N >::m_c

private

The centroid of the simplex (ex_cluding the worst point).

◆ m_gamma

template<typename Real, Integer N>

Real Optimist::Optimizer::NelderMead< Real, N >::m_gamma {2.0}

private

Nelder-Mead reflection coefficient.

◆ m_rho

template<typename Real, Integer N>

Real Optimist::Optimizer::NelderMead< Real, N >::m_rho {0.5}

private

Nelder-Mead expansion coefficient.

◆ m_s

template<typename Real, Integer N>

Simplex Optimist::Optimizer::NelderMead< Real, N >::m_s

private

Simplex representing the vertices of the simplex.

◆ m_sigma

template<typename Real, Integer N>

Real Optimist::Optimizer::NelderMead< Real, N >::m_sigma {0.5}

private

Nelder-Mead contraction coefficient.

◆ requires_first_derivative

template<typename Real, Integer N>

bool Optimist::Optimizer::NelderMead< Real, N >::requires_first_derivative {false}

staticconstexpr

◆ requires_function

template<typename Real, Integer N>

bool Optimist::Optimizer::NelderMead< Real, N >::requires_function {true}

staticconstexpr

◆ requires_second_derivative

template<typename Real, Integer N>

bool Optimist::Optimizer::NelderMead< Real, N >::requires_second_derivative {false}

staticconstexpr

The documentation for this class was generated from the following file:

include/Optimist/Optimizer/NelderMead.hh

Public Types

Public Member Functions

Static Public Attributes

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Simplex

Constructor & Destructor Documentation

◆ NelderMead()

Member Function Documentation

◆ centroid()

◆ expansion()

◆ initialize()

◆ inward_contraction()

◆ name_impl()

◆ outward_contraction()

◆ reflection()

◆ shrink()

◆ solve_impl()

◆ sort()

Member Data Documentation

◆ m_alpha

◆ m_c

◆ m_gamma

◆ m_rho

◆ m_s

◆ m_sigma

◆ requires_first_derivative

◆ requires_function

◆ requires_second_derivative