Class container for the multi-dimensional optimizer. More...

#include <Optimizer.hh>

Inherits Optimist::SolverBase< T, TypeTrait< T >::Scalar, DerivedSolver >.

Public Types
using	Scalar = typename TypeTrait<T>::Scalar
using	Input = T
using	Output = Scalar
Public Types inherited from Optimist::SolverBase< T, TypeTrait< T >::Scalar, DerivedSolver >
using	InputTrait
using	OutputTrait
using	Scalar
using	FirstDerivative
using	SecondDerivative

Public Member Functions
	Optimizer ()
constexpr std::string	name () const
Integer	gradient_evaluations () const
Integer	max_gradient_evaluations () const
void	max_gradient_evaluations (const Integer t_gradient_evaluations)
Integer	hessian_evaluations () const
Integer	max_hessian_evaluations () const
void	max_hessian_evaluations (const Integer t_hessian_evaluations)
Public Member Functions inherited from Optimist::SolverBase< T, TypeTrait< T >::Scalar, DerivedSolver >
	SolverBase ()
void	reset_bounds (const Integer n=InputTrait::IsDynamic ? 0 :InputTrait::Dimension)
const T &	lower_bound () const
const T &	upper_bound () const
void	bounds (const T &t_lower_bound, const T &t_upper_bound)
constexpr Integer	input_dimension () const
constexpr Integer	output_dimension () const
Integer	function_evaluations () const
void	max_function_evaluations (const Integer t_max_function_evaluations)
Integer	iterations () const
Integer	max_iterations () const
Scalar	alpha () const
Integer	relaxations () const
Integer	max_relaxations () const
Scalar	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
std::ostream &	ostream () const
bool	solve (FunctionLambda &&function, const T &x_ini, T &x_sol)
bool	rootfind (const FunctionBase< FunctionInput, FunctionOutput, DerivedFunction > &function, const T &x_ini, T &x_sol)
bool	optimize (const FunctionBase< FunctionInput, FunctionOutput, DerivedFunction > &function, const T &x_ini, T &x_sol)
constexpr std::string	name () const

Static Public Attributes
static constexpr bool	IsRootFinder {false}
static constexpr bool	IsOptimizer {true}

Protected Member Functions
template<typename GradientLambda>
bool	evaluate_gradient (GradientLambda &&gradient, const Input &x, FirstDerivative &out)
template<typename HessianLambda>
bool	evaluate_hessian (HessianLambda &&hessian, const Input &x, SecondDerivative &out)
template<typename FunctionLambda>
bool	solve (FunctionLambda &&function, const Input &x_ini, Output &x_sol)
template<typename FunctionLambda, typename GradientLambda>
bool	solve (FunctionLambda &&function, GradientLambda &&gradient, const Input &x_ini, Output &x_sol)
template<typename FunctionLambda, typename GradientLambda, typename HessianLambda>
bool	solve (FunctionLambda &&function, GradientLambda &&gradient, HessianLambda &&hessian, const Input &x_ini, Output &x_sol)
Protected Member Functions inherited from Optimist::SolverBase< T, TypeTrait< T >::Scalar, DerivedSolver >
Integer	first_derivative_evaluations () const
Integer	max_first_derivative_evaluations () const
Integer	second_derivative_evaluations () const
Integer	max_second_derivative_evaluations () const
void	reset_counters ()
bool	evaluate_function (FunctionLambda &&function, const T &x, TypeTrait< T >::Scalar &out)
bool	evaluate_first_derivative (FirstDerivativeLambda &&function, const T &x, FirstDerivative &out)
bool	evaluate_second_derivative (SecondDerivativeLambda &&function, const T &x, SecondDerivative &out)
bool	damp (FunctionLambda &&function, const T &x_old, const T &function_old, const T &step_old, T &x_new, T &function_new, T &step_new)
void	header ()
void	bottom ()
void	info (Scalar residuals, const std::string &notes="-")

Friends
class	SolverBase< T, typename TypeTrait< T >::Scalar, DerivedSolver >

Additional Inherited Members
Protected Attributes inherited from Optimist::SolverBase< T, TypeTrait< T >::Scalar, DerivedSolver >
T	m_lower_bound
T	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
Scalar	m_alpha
Integer	m_relaxations
Integer	m_max_relaxations
Scalar	m_tolerance
bool	m_verbose
bool	m_damped
std::ostream *	m_ostream
std::string	m_task
bool	m_converged

Detailed Description

template<typename T, typename DerivedSolver>
requires (TypeTrait<T>::IsScalar || TypeTrait<T>::IsEigen) && (!TypeTrait<T>::IsFixed || TypeTrait<T>::Dimension > 0)
class Optimist::Optimizer::Optimizer< T, DerivedSolver >

Optimizer

This section describes the scalar optimizers implemented in Optimist. The available optimizers are derivative and non-derivative methods. Derivative methods employ the function's derivative to find the minimum with high accuracy, while non-derivative methods approximate the derivative for improved efficiency in certain scenarios.

Here, the solvers are implemented for solving problems of the form

\[ \min_{\mathbf{x}} \mathbf{f}(\mathbf{x}) = 0 \quad \text{with} \quad \mathbf{f}: \mathbb{R}^n \rightarrow \mathbb{R} \text{,} \]

which consist in finding the minimum of the cost function \(\mathbf{f}\) by iteratively updating the current iterate \(\mathbf{x}_k\) until convergence is achieved. The solvers require the cost function \(\mathbf{f}\) and its first derivative \(\mathbf{f}^{\prime}(\mathbf{x})\) to be provided by the user. Alternatively, the derivative can be approximated numerically using finite differences, depending on the problem's complexity and the user's preference.

Template Parameters

T	Input type (scalar or Eigen vector).
DerivedSolver	Derived solver class.

Member Typedef Documentation

◆ Input

template<typename T, typename DerivedSolver>

using Optimist::Optimizer::Optimizer< T, DerivedSolver >::Input = T

◆ Output

template<typename T, typename DerivedSolver>

using Optimist::Optimizer::Optimizer< T, DerivedSolver >::Output = Scalar

◆ Scalar

template<typename T, typename DerivedSolver>

using Optimist::Optimizer::Optimizer< T, DerivedSolver >::Scalar = typename TypeTrait<T>::Scalar

Constructor & Destructor Documentation

◆ Optimizer()

template<typename T, typename DerivedSolver>

Optimist::Optimizer::Optimizer< T, DerivedSolver >::Optimizer ( )

inline

Class constructor for the multi-dimensional optimizer.

Member Function Documentation

◆ evaluate_gradient()

template<typename T, typename DerivedSolver>

template<typename GradientLambda>

bool Optimist::Optimizer::Optimizer< T, DerivedSolver >::evaluate_gradient	(	GradientLambda &&	gradient,
		const Input &	x,
		FirstDerivative &	out )

inlineprotected

Evaluate the gradient function.

Template Parameters

GradientLambda The gradient lambda function type.

Parameters

[in]	gradient	Gradient lambda function.
[in]	x	Input point.
[out]	out	Gradient value.

Returns: The boolean flag for successful evaluation.

◆ evaluate_hessian()

template<typename T, typename DerivedSolver>

template<typename HessianLambda>

bool Optimist::Optimizer::Optimizer< T, DerivedSolver >::evaluate_hessian	(	HessianLambda &&	hessian,
		const Input &	x,
		SecondDerivative &	out )

inlineprotected

Evaluate the hessian function.

Template Parameters

HessianLambda The hessian lambda function type.

Parameters

[in]	hessian	Hessian lambda function.
[in]	x	Input point.
[out]	out	Hessian value.

Returns: The boolean flag for successful evaluation.

◆ gradient_evaluations()

template<typename T, typename DerivedSolver>

Integer Optimist::Optimizer::Optimizer< T, DerivedSolver >::gradient_evaluations ( ) const

inline

Get the number of gradient evaluations.

Returns: The number of gradient evaluations.

◆ hessian_evaluations()

template<typename T, typename DerivedSolver>

Integer Optimist::Optimizer::Optimizer< T, DerivedSolver >::hessian_evaluations ( ) const

inline

Get the number of hessian evaluations.

Returns: The number of hessian evaluations.

◆ max_gradient_evaluations() [1/2]

template<typename T, typename DerivedSolver>

Integer Optimist::Optimizer::Optimizer< T, DerivedSolver >::max_gradient_evaluations ( ) const

inline

Get the number of maximum allowed gradient evaluations.

Returns: The number of maximum allowed gradient evaluations.

◆ max_gradient_evaluations() [2/2]

template<typename T, typename DerivedSolver>

void Optimist::Optimizer::Optimizer< T, DerivedSolver >::max_gradient_evaluations ( const Integer t_gradient_evaluations )

inline

Set the number of maximum allowed gradient evaluations.

Parameters

[in] t_gradient_evaluations The number of maximum allowed gradient evaluations.

◆ max_hessian_evaluations() [1/2]

template<typename T, typename DerivedSolver>

Integer Optimist::Optimizer::Optimizer< T, DerivedSolver >::max_hessian_evaluations ( ) const

inline

Get the number of maximum allowed hessian evaluations.

Returns: The number of maximum allowed hessian evaluations.

◆ max_hessian_evaluations() [2/2]

template<typename T, typename DerivedSolver>

void Optimist::Optimizer::Optimizer< T, DerivedSolver >::max_hessian_evaluations ( const Integer t_hessian_evaluations )

inline

Set the number of maximum allowed hessian evaluations.

Parameters

[in] t_hessian_evaluations The number of maximum allowed hessian evaluations.

◆ name()

template<typename T, typename DerivedSolver>

std::string Optimist::Optimizer::Optimizer< T, DerivedSolver >::name ( ) const

inlineconstexpr

Get the solver name.

Returns: The solver name.

◆ solve() [1/3]

template<typename T, typename DerivedSolver>

template<typename FunctionLambda>

bool Optimist::Optimizer::Optimizer< T, DerivedSolver >::solve	(	FunctionLambda &&	function,
		const Input &	x_ini,
		Output &	x_sol )

inlineprotected

Solve the root-finding problem given the function, and without derivatives.

Template Parameters

FunctionLambda The lambda function type.

Parameters

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

Returns: The convergence boolean flag.

◆ solve() [2/3]

template<typename T, typename DerivedSolver>

template<typename FunctionLambda, typename GradientLambda>

bool Optimist::Optimizer::Optimizer< T, DerivedSolver >::solve	(	FunctionLambda &&	function,
		GradientLambda &&	gradient,
		const Input &	x_ini,
		Output &	x_sol )

inlineprotected

Solve the root-finding problem given the function, and its gradient.

Template Parameters

FunctionLambda	The lambda function type.
GradientLambda	The gradient lambda function type.

Parameters

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

Returns: The convergence boolean flag.

◆ solve() [3/3]

template<typename T, typename DerivedSolver>

template<typename FunctionLambda, typename GradientLambda, typename HessianLambda>

bool Optimist::Optimizer::Optimizer< T, DerivedSolver >::solve	(	FunctionLambda &&	function,
		GradientLambda &&	gradient,
		HessianLambda &&	hessian,
		const Input &	x_ini,
		Output &	x_sol )

inlineprotected

Solve the root-finding problem given the function, and its gradient and Hessian.

Template Parameters

FunctionLambda	The lambda function type.
GradientLambda	The gradient lambda function type.
HessianLambda	The hessian lambda function type.

Parameters

[in]	function	Function lambda.
[in]	gradient	Gradient lambda function.
[in]	hessian	Hessian lambda function.
[in]	x_ini	Initialization point.
[out]	x_sol	Solution point.

Returns: The convergence boolean flag.

◆ SolverBase< T, typename TypeTrait< T >::Scalar, DerivedSolver >

template<typename T, typename DerivedSolver>

friend class SolverBase< T, typename TypeTrait< T >::Scalar, DerivedSolver >

friend

Member Data Documentation

◆ IsOptimizer

template<typename T, typename DerivedSolver>

bool Optimist::Optimizer::Optimizer< T, DerivedSolver >::IsOptimizer {true}

staticconstexpr

◆ IsRootFinder

template<typename T, typename DerivedSolver>

bool Optimist::Optimizer::Optimizer< T, DerivedSolver >::IsRootFinder {false}

staticconstexpr

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

core/include/Optimist/Optimizer.hh

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Friends

Additional Inherited Members

Detailed Description

Optimizer

Member Typedef Documentation

◆ Input

◆ Output

◆ Scalar

Constructor & Destructor Documentation

◆ Optimizer()

Member Function Documentation

◆ evaluate_gradient()

◆ evaluate_hessian()

◆ gradient_evaluations()

◆ hessian_evaluations()

◆ max_gradient_evaluations() [1/2]

◆ max_gradient_evaluations() [2/2]

◆ max_hessian_evaluations() [1/2]

◆ max_hessian_evaluations() [2/2]

◆ name()

◆ solve() [1/3]

◆ solve() [2/3]

◆ solve() [3/3]

Friends And Related Symbol Documentation

◆ SolverBase< T, typename TypeTrait< T >::Scalar, DerivedSolver >

Member Data Documentation

◆ IsOptimizer

◆ IsRootFinder