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

#include <Optimizer.hh>

Inherits Optimist::SolverBase< Real, N, 1, DerivedSolver, false >.

Public Types
using	Vector = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::InputType
using	RowVector = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::FirstDerivativeType
using	Matrix = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::SecondDerivativeType
using	FunctionWrapper = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::FunctionWrapper
using	GradientWrapper = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::FirstDerivativeWrapper
using	HessianWrapper = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::SecondDerivativeWrapper

Public Member Functions
	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::SolverBase< Real, N, 1, DerivedSolver, 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	is_rootfinder {false}
static constexpr bool	is_optimizer {true}
static constexpr bool	requires_function {DerivedSolver::requires_function}
static constexpr bool	requires_first_derivative {DerivedSolver::requires_first_derivative}
static constexpr bool	requires_second_derivative {DerivedSolver::requires_second_derivative}

Protected Member Functions
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::SolverBase< Real, N, 1, DerivedSolver, 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="-")

Friends
class	SolverBase< Real, N, 1, Optimizer< Real, N, DerivedSolver, ForceEigen > >

Additional Inherited Members
Protected Types inherited from Optimist::SolverBase< Real, N, 1, DerivedSolver, false >
using	InputType
using	OutputType
using	TraceType
using	FirstDerivativeType
using	SecondDerivativeType
using	FunctionWrapper
using	FirstDerivativeWrapper
using	SecondDerivativeWrapper
Protected Attributes inherited from Optimist::SolverBase< Real, N, 1, DerivedSolver, 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, typename DerivedSolver, bool ForceEigen = false>
class Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >

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

N	Dimension of the optimization problem.
DerivedSolver	Derived solver class.
ForceEigen	Force the use of Eigen types for input and output.

Member Typedef Documentation

◆ FunctionWrapper

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

using Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::FunctionWrapper = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::FunctionWrapper

◆ GradientWrapper

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

using Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::GradientWrapper = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::FirstDerivativeWrapper

◆ HessianWrapper

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

using Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::HessianWrapper = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::SecondDerivativeWrapper

◆ Matrix

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

using Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::Matrix = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::SecondDerivativeType

Hessian matrix type.

◆ RowVector

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

using Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::RowVector = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::FirstDerivativeType

Gradient (row) vector type.

◆ Vector

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

using Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::Vector = typename SolverBase<Real, N, 1, DerivedSolver, ForceEigen>::InputType

Vector type.

Constructor & Destructor Documentation

◆ Optimizer()

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::Optimizer ( )

inline

Class constructor for the multi-dimensional optimizer.

Member Function Documentation

◆ evaluate_gradient()

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

void Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::evaluate_gradient	(	GradientWrapper	gradient,
		const Vector &	x,
		Matrix &	out )

inlineprotected

Evaluate the gradient function.

Parameters

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

◆ evaluate_hessian()

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

void Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::evaluate_hessian	(	HessianWrapper	hessian,
		const Vector &	x,
		Matrix &	out )

inlineprotected

Evaluate the hessian function.

Parameters

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

◆ gradient_evaluations()

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::gradient_evaluations ( ) const

inline

Get the number of gradient evaluations.

Returns: The number of gradient evaluations.

◆ hessian_evaluations()

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::hessian_evaluations ( ) const

inline

Get the number of hessian evaluations.

Returns: The number of hessian evaluations.

◆ max_gradient_evaluations() [1/2]

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::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 Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

void Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::max_gradient_evaluations ( 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 Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

Integer Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::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 Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

void Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::max_hessian_evaluations ( 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 Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

std::string Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::name ( ) const

inline

Get the solver name.

Returns: The solver name.

◆ solve() [1/3]

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::solve	(	FunctionWrapper	function,
		GradientWrapper	gradient,
		HessianWrapper	hessian,
		Vector const &	x_ini,
		Vector &	x_sol )

inlineprotected

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

Parameters

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

Returns: The convergence boolean flag.

◆ solve() [2/3]

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::solve	(	FunctionWrapper	function,
		GradientWrapper	gradient,
		Vector const &	x_ini,
		Vector &	x_sol )

inlineprotected

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

Parameters

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

Returns: The convergence boolean flag.

◆ solve() [3/3]

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::solve	(	FunctionWrapper	function,
		Vector const &	x_ini,
		Vector &	x_sol )

inlineprotected

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

Parameters

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

Returns: The convergence boolean flag.

◆ SolverBase< Real, N, 1, Optimizer< Real, N, DerivedSolver, ForceEigen > >

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

friend class SolverBase< Real, N, 1, Optimizer< Real, N, DerivedSolver, ForceEigen > >

friend

Member Data Documentation

◆ is_optimizer

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::is_optimizer {true}

staticconstexpr

◆ is_rootfinder

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::is_rootfinder {false}

staticconstexpr

◆ requires_first_derivative

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::requires_first_derivative {DerivedSolver::requires_first_derivative}

staticconstexpr

◆ requires_function

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::requires_function {DerivedSolver::requires_function}

staticconstexpr

◆ requires_second_derivative

template<typename Real, Integer N, typename DerivedSolver, bool ForceEigen = false>

bool Optimist::Optimizer::Optimizer< Real, N, DerivedSolver, ForceEigen >::requires_second_derivative {DerivedSolver::requires_second_derivative}

staticconstexpr

Basic constants.

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

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

◆ FunctionWrapper

◆ GradientWrapper

◆ HessianWrapper

◆ Matrix

◆ RowVector

◆ Vector

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< Real, N, 1, Optimizer< Real, N, DerivedSolver, ForceEigen > >

Member Data Documentation

◆ is_optimizer

◆ is_rootfinder

◆ requires_first_derivative

◆ requires_function

◆ requires_second_derivative