Implements the Nelder-Mead optimization algorithm for nonlinear optimization problems. More...

#include <Utils_NelderMead.hh>

Public Types
using	Vec_t = Eigen::Matrix<Real,Eigen::Dynamic,1>

using	Mat_t = Eigen::Matrix<Real,Eigen::Dynamic,Eigen::Dynamic>

using	MapVec = Eigen::Map<Vec_t>

using	MapMat = Eigen::Map<Mat_t>

using	integer = int

using	NMFunc = std::function<Real(Real const[])>

using	NM_move

Public Member Functions
	NelderMead (string_view name)
	Constructor that initializes the NelderMead instance with a specific name.

string_view	name (void) const
	Get the name of the class.

void	setup (integer dim, NMFunc &fun, Console const *console)
	Setup the optimizer with the function and console interface.

void	change_console (Console const *console)
	Change the console output interface.

void	set_verbose (integer level)
	Set the verbosity level for logging during the optimization process.

void	set_tolerance (Real tol)
	Set the tolerance for stopping criteria in the optimization process.

void	set_max_iterations (integer mit)
	Set the maximum number of iterations allowed in the optimization process.

void	set_max_fun_evaluation (integer mfev)
	Set the maximum number of function evaluations allowed in the optimization process.

void	message (Real tol) const
	Display a message with information about the current tolerance level.

string	info () const
	Provide information about the current state of the Nelder-Mead optimization.

void	print_info (ostream_type &stream) const
	Print detailed information about the current state of the Nelder-Mead optimizer.

bool	search ()
	Perform the search step of the optimization process.

bool	run (Real const x_sol[], Real h)
	Run the optimization process starting from an initial guess and step size.

Real	get_last_solution (Real x[]) const
	Get the solution found by the Nelder-Mead algorithm after the last run.

Real	get_better_value () const
	Get the best function value found during the optimization process.

Real	get_worst_value () const
	Get the worst function value encountered during the optimization process.

Static Public Member Functions
static string	to_string (NM_move n)

Detailed Description

template<typename Real>
class Utils::NelderMead< Real >

Implements the Nelder-Mead optimization algorithm for nonlinear optimization problems.

The Nelder-Mead algorithm is a widely used simplex-based method for minimizing an objective function in multiple dimensions. It is especially useful for problems where derivative information is not readily available or when the objective function is noisy.

Template Parameters

Real	The numeric type used for calculations, typically `float` or `double`.

This implementation of the Nelder-Mead algorithm is based on several foundational works:

J.A. Nelder and R. Mead, "A Simplex Method for Function Minimization," Computer Journal, vol. 7, pp. 308-313, 1965.
L.A. Yarbro and S.N. Deming, "Optimization by the Simplex Method," Analytica Chimica Acta, vol. 73, pp. 391-398, 1974.
S.L.S. Jacoby, J.S. Kowalik, and J.T. Pizzo, Iterative Methods for Nonlinear Optimization Problems (Englewood Cliffs, NJ: Prentice-Hall), 1972.

Note: The Nelder-Mead algorithm does not require derivatives, making it suitable for non-smooth or noisy functions.

Member Typedef Documentation

◆ integer

template<typename Real>

using Utils::NelderMead< Real >::integer = int

◆ MapMat

template<typename Real>

using Utils::NelderMead< Real >::MapMat = Eigen::Map<Mat_t>

◆ MapVec

template<typename Real>

using Utils::NelderMead< Real >::MapVec = Eigen::Map<Vec_t>

◆ Mat_t

template<typename Real>

using Utils::NelderMead< Real >::Mat_t = Eigen::Matrix<Real,Eigen::Dynamic,Eigen::Dynamic>

◆ NM_move

template<typename Real>

using Utils::NelderMead< Real >::NM_move

Initial value:

 enum class NelderMead_move : integer {
      INIT,
      REFLECT,
      EXPAND_FE,
      EXPAND_FR,
      CONTRACT_O,
      CONTRACT_I,
      SHRINK,
      RESTART,
      WORSE
    }

◆ NMFunc

template<typename Real>

using Utils::NelderMead< Real >::NMFunc = std::function<Real(Real const[])>

◆ Vec_t

template<typename Real>

using Utils::NelderMead< Real >::Vec_t = Eigen::Matrix<Real,Eigen::Dynamic,1>

Constructor & Destructor Documentation

◆ NelderMead()

template<typename Real>

Utils::NelderMead< Real >::NelderMead ( string_view name )

inlineexplicit

Constructor that initializes the NelderMead instance with a specific name.

Parameters

name	The name to be assigned to this instance of the Nelder-Mead optimizer.

Member Function Documentation

◆ change_console()

template<typename Real>

void Utils::NelderMead< Real >::change_console ( Console const * console )

inline

Change the console output interface.

Parameters

console A pointer to the new console object for logging.

◆ get_better_value()

template<typename Real>

Real Utils::NelderMead< Real >::get_better_value ( ) const

inline

Get the best function value found during the optimization process.

Returns: The best (lowest) function value found.

◆ get_last_solution()

template<typename Real>

Real Utils::NelderMead< Real >::get_last_solution ( Real x[] ) const

inline

Get the solution found by the Nelder-Mead algorithm after the last run.

Parameters

x	An array to store the solution values (the optimizer writes the solution here).

Returns: The function value at the solution point.

◆ get_worst_value()

template<typename Real>

Real Utils::NelderMead< Real >::get_worst_value ( ) const

inline

Get the worst function value encountered during the optimization process.

Returns: The worst (highest) function value found.

◆ info()

template<typename Real>

string Utils::NelderMead< Real >::info ( ) const

Provide information about the current state of the Nelder-Mead optimization.

Returns: A string with detailed information about the current state of the optimizer.

◆ message()

template<typename Real>

void Utils::NelderMead< Real >::message ( Real tol ) const

Display a message with information about the current tolerance level.

Parameters

tol	The tolerance level for which a message should be displayed.

◆ name()

template<typename Real>

string_view Utils::NelderMead< Real >::name ( void ) const

inline

Get the name of the class.

Returns: A string representing the name of the Nelder-Mead optimizer instance.

◆ print_info()

template<typename Real>

void Utils::NelderMead< Real >::print_info ( ostream_type & stream ) const

inline

Print detailed information about the current state of the Nelder-Mead optimizer.

Parameters

stream The output stream where the information will be printed.

◆ run()

template<typename Real>

bool Utils::NelderMead< Real >::run	(	Real const	x_sol[],
		Real	h )

Run the optimization process starting from an initial guess and step size.

Parameters

x_sol	An array containing the initial guess for the solution.
h	The initial step size for the simplex search.

Returns: True if the optimization converged successfully; otherwise, false.

◆ search()

template<typename Real>

bool Utils::NelderMead< Real >::search ( )

Perform the search step of the optimization process.

Returns: True if the search was successful; otherwise, false.

◆ set_max_fun_evaluation()

template<typename Real>

void Utils::NelderMead< Real >::set_max_fun_evaluation ( integer mfev )

Set the maximum number of function evaluations allowed in the optimization process.

Parameters

mfev	The maximum number of function evaluations.

◆ set_max_iterations()

template<typename Real>

void Utils::NelderMead< Real >::set_max_iterations ( integer mit )

Set the maximum number of iterations allowed in the optimization process.

Parameters

mit	The maximum number of iterations to be performed.

◆ set_tolerance()

template<typename Real>

void Utils::NelderMead< Real >::set_tolerance ( Real tol )

Set the tolerance for stopping criteria in the optimization process.

Parameters

tol	The tolerance value, typically a small positive number (e.g., 1e-6).

◆ set_verbose()

template<typename Real>

void Utils::NelderMead< Real >::set_verbose ( integer level )

inline

Set the verbosity level for logging during the optimization process.

Parameters

level The verbosity level (higher values produce more detailed output).

◆ setup()

template<typename Real>

void Utils::NelderMead< Real >::setup	(	integer	dim,
		NMFunc &	fun,
		Console const *	console )

Setup the optimizer with the function and console interface.

Parameters

dim	The dimensionality of the optimization problem.
fun	A reference to the function to be minimized.
console	A pointer to the console for output logging during optimization.

◆ to_string()

template<typename Real>

static string Utils::NelderMead< Real >::to_string ( NM_move n )

inlinestatic

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

/Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/UtilsLite/src/Utils_NelderMead.hh
/Users/enricobertolazzi/Ricerca/PINS/PINS-submodules/UtilsLite/src/Utils_NelderMead.cc

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ integer

◆ MapMat

◆ MapVec

◆ Mat_t

◆ NM_move

◆ NMFunc

◆ Vec_t

Constructor & Destructor Documentation

◆ NelderMead()

Member Function Documentation

◆ change_console()

◆ get_better_value()

◆ get_last_solution()

◆ get_worst_value()

◆ info()

◆ message()

◆ name()

◆ print_info()

◆ run()

◆ search()

◆ set_max_fun_evaluation()

◆ set_max_iterations()

◆ set_tolerance()

◆ set_verbose()

◆ setup()

◆ to_string()