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

#include <NelderMead.hh>

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

Public Types
using	Vector = typename Optimizer<Real, N, NelderMead<Real, N>>::Vector
using	Matrix = typename Optimizer<Real, N, NelderMead<Real, N>>::Matrix
using	FunctionWrapper = typename Optimizer<Real, N, NelderMead<Real, N>>::FunctionWrapper
using	Simplex = std::vector<Vector>
Public Types inherited from Optimist::Optimizer::Optimizer< Real, N, NelderMead< Real, N > >
using	Vector
using	RowVector
using	Matrix
using	FunctionWrapper
using	GradientWrapper
using	HessianWrapper

Public Member Functions
	NelderMead ()
std::string	name_impl () const
void	initialize (const Vector &x_ini, Real delta)
Vector	centroid () const
void	sort (FunctionWrapper function)
	Sort the points of the simplex based on the function values and updates the centroid.
Vector	reflection () const
	Computes the reflection point.
Vector	expansion (const Vector &x) const
	Computes the expansion point.
Vector	outward_contraction (const Vector &x) const
Vector	inward_contraction () const
void	shrink ()
bool	solve_impl (FunctionWrapper 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 ()
const InputType &	lower_bound () const
const InputType &	upper_bound () const
void	bounds (const InputType &t_lower_bound, const InputType &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 (FunctionWrapper function, const InputType &x_ini, InputType &x_sol)
bool	rootfind (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, const InputType &x_ini, InputType &x_sol)
bool	optimize (FunctionBase< Real, FunInDim, FunOutDim, DerivedFunction, ForceEigen &&FunOutDim==1 > const &function, const InputType &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
static constexpr bool	requires_function
static constexpr bool	requires_first_derivative
static constexpr bool	requires_second_derivative

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 Types inherited from Optimist::SolverBase< Real, N, 1, NelderMead< Real, N >, false >
using	InputType
using	OutputType
using	TraceType
using	FirstDerivativeType
using	SecondDerivativeType
using	FunctionWrapper
using	FirstDerivativeWrapper
using	SecondDerivativeWrapper
Protected Member Functions inherited from Optimist::Optimizer::Optimizer< Real, N, NelderMead< Real, N > >
void	evaluate_gradient (GradientWrapper gradient, const Vector &x, Matrix &out)
void	evaluate_hessian (HessianWrapper hessian, const Vector &x, Matrix &out)
bool	solve (FunctionWrapper 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 ()
void	evaluate_function (FunctionWrapper function, const InputType &x, OutputType &out)
void	evaluate_first_derivative (FirstDerivativeWrapper function, const InputType &x, FirstDerivativeType &out)
void	evaluate_second_derivative (SecondDerivativeWrapper function, const InputType &x, SecondDerivativeType &out)
void	store_trace (const InputType &x)
bool	damp (FunctionWrapper 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

◆ FunctionWrapper

template<typename Real, Integer N>

using Optimist::Optimizer::NelderMead< Real, N >::FunctionWrapper = typename Optimizer<Real, N, NelderMead<Real, N>>::FunctionWrapper

◆ Matrix

template<typename Real, Integer N>

using Optimist::Optimizer::NelderMead< Real, N >::Matrix = typename Optimizer<Real, N, NelderMead<Real, N>>::Matrix

◆ Simplex

template<typename Real, Integer N>

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

Simplex type.

◆ Vector

template<typename Real, Integer N>

using Optimist::Optimizer::NelderMead< Real, N >::Vector = typename Optimizer<Real, N, NelderMead<Real, N>>::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 ( const Vector & x ) const

inline

Parameters

x	The reflection point.

Returns: The expansion point.

◆ initialize()

template<typename Real, Integer N>

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

inline

Initialize the simplex around a given centroid.

Parameters

x_ini	The initial point.
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 ( const Vector & x ) const

inline

Computes the outward contraction point.

Parameters

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	(	FunctionWrapper	function,
		Vector const &	x_ini,
		Vector &	x_sol )

inline

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

Parameters

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

Returns: The convergence boolean flag.

◆ sort()

template<typename Real, Integer N>

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

inline

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

◆ FunctionWrapper

◆ Matrix

◆ Simplex

◆ Vector

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