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

void	max_gradient_evaluations (Integer t_gradient_evaluations)

Integer	hessian_evaluations () const

Integer	max_hessian_evaluations () const

void	max_hessian_evaluations (Integer t_hessian_evaluations)

Public Member Functions inherited from Optimist::Solver< Real, N, 1, NelderMead< Real, N > >
	Solver ()

	Solver (FunctionWrapper function, const InputType &x_ini, InputType &x_sol)

	Solver (FunctionWrapper function, FirstDerivativeWrapper first_derivative, const InputType &x_ini, InputType &x_sol)

	Solver (FunctionWrapper function, FirstDerivativeWrapper first_derivative, SecondDerivativeWrapper second_derivative, const InputType &x_ini, InputType &x_sol)

const InputType &	lower_bound () const

void	lower_bound (const InputType &t_lower_bound)

const InputType &	upper_bound () const

void	upper_bound (const InputType &t_upper_bound)

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	max_function_evaluations () const

Integer	iterations () const

Integer	max_iterations () const

void	max_iterations (Integer t_max_iterations)

Real	alpha () const

void	alpha (Real t_alpha)

Integer	relaxations () const

Integer	max_relaxations () const

void	max_relaxations (Integer t_max_relaxations)

Real	tolerance () const

void	tolerance (Real t_tolerance)

void	verbose_mode (bool t_verbose)

bool	verbose_mode () const

void	enable_verbose_mode ()

void	disable_verbose_mode ()

void	damped_mode (bool t_damped)

bool	damped_mode () const

void	enable_damped_mode ()

void	disable_damped_mode ()

std::string	task () const

void	task (std::string t_task)

bool	converged () const

const TraceType &	trace () const

std::ostream &	ostream () const

void	ostream (std::ostream &t_ostream)

bool	solve (FunctionWrapper function, const InputType &x_ini, InputType &x_sol)

bool	solve (FunctionWrapper function, FirstDerivativeWrapper first_derivative, const InputType &x_ini, InputType &x_sol)

bool	solve (FunctionWrapper function, FirstDerivativeWrapper first_derivative, SecondDerivativeWrapper second_derivative, const InputType &x_ini, InputType &x_sol)

bool	rootfind (Function< Real, FunInDim, FunOutDim, DerivedFunction > const &function, const InputType &x_ini, InputType &x_sol)

bool	optimize (Function< Real, FunInDim, FunOutDim, DerivedFunction > 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
Public Attributes inherited from Optimist::Optimizer::Optimizer< Real, N, NelderMead< Real, N > >
friend	Solver< Real, N, 1, Optimizer< Real, N, DerivedSolver > >

Protected Types inherited from Optimist::Solver< Real, N, 1, NelderMead< Real, N > >
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)

bool	solve (FunctionWrapper function, GradientWrapper gradient, Vector const &x_ini, Vector &x_sol)

bool	solve (FunctionWrapper function, GradientWrapper gradient, HessianWrapper hessian, Vector const &x_ini, Vector &x_sol)

Protected Member Functions inherited from Optimist::Solver< Real, N, 1, NelderMead< Real, N > >
Integer	first_derivative_evaluations () const

Integer	max_first_derivative_evaluations () const

void	max_first_derivative_evaluations (Integer first_derivative_evaluations)

Integer	second_derivative_evaluations () const

Integer	max_second_derivative_evaluations () const

void	max_second_derivative_evaluations (Integer second_derivative_evaluations)

bool	solve (Function< Real, FunInDim, FunOutDim, DerivedFunction > const &function, const InputType &x_ini, InputType &x_sol, bool is_optimization)

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::Solver< Real, N, 1, NelderMead< Real, N > >
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