Class container for the QuasiNewton's method. More...

#include <QuasiNewton.hh>

Inherits Optimist::RootFinder::RootFinder< Vector, DerivedSolver >.

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

Public Member Functions
	QuasiNewton ()
constexpr std::string	name_impl () const
template<typename FunctionLambda, typename JacobianLambda>
bool	solve_impl (FunctionLambda &&function, JacobianLambda &&jacobian, const Vector &x_ini, Vector &x_sol)
void	update (const Vector &delta_x_old, const Vector &delta_function_old, const FirstDerivative &jacobian_old, const Vector &delta_x_new, const Vector &delta_function_new, const Vector &function_new, FirstDerivative &jacobian_new)
Public Member Functions inherited from Optimist::RootFinder::RootFinder< Vector, DerivedSolver >
	RootFinder ()
constexpr std::string	name () const
Integer	jacobian_evaluations () const
Integer	max_jacobian_evaluations () const
Integer	hessian_evaluations () const
Integer	max_hessian_evaluations () const
bool	solve (FunctionLambda &&function, const Input &x_ini, Output &x_sol)
Public Member Functions inherited from Optimist::SolverBase< Vector, Vector, DerivedSolver >
	SolverBase ()
void	reset_bounds (const Integer n=InputTrait::IsDynamic ? 0 :InputTrait::Dimension)
const Vector &	lower_bound () const
const Vector &	upper_bound () const
void	bounds (const Vector &t_lower_bound, const Vector &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 Vector &x_ini, Vector &x_sol)
bool	rootfind (const FunctionBase< FunctionInput, FunctionOutput, DerivedFunction > &function, const Vector &x_ini, Vector &x_sol)
bool	optimize (const FunctionBase< FunctionInput, FunctionOutput, DerivedFunction > &function, const Vector &x_ini, Vector &x_sol)
constexpr std::string	name () const

Additional Inherited Members
Static Public Attributes inherited from Optimist::RootFinder::RootFinder< Vector, DerivedSolver >
static constexpr bool	IsRootFinder
static constexpr bool	IsOptimizer
Protected Member Functions inherited from Optimist::RootFinder::RootFinder< Vector, DerivedSolver >
bool	evaluate_jacobian (JacobianLambda &&jacobian, const Input &x, FirstDerivative &out)
bool	evaluate_hessian (HessianLambda &&hessian, const Input &x, SecondDerivative &out)
Protected Member Functions inherited from Optimist::SolverBase< Vector, Vector, 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 Vector &x, Vector &out)
bool	evaluate_first_derivative (FirstDerivativeLambda &&function, const Vector &x, FirstDerivative &out)
bool	evaluate_second_derivative (SecondDerivativeLambda &&function, const Vector &x, SecondDerivative &out)
bool	damp (FunctionLambda &&function, const Vector &x_old, const Vector &function_old, const Vector &step_old, Vector &x_new, Vector &function_new, Vector &step_new)
void	header ()
void	bottom ()
void	info (Scalar residuals, const std::string &notes="-")
Protected Attributes inherited from Optimist::SolverBase< Vector, Vector, DerivedSolver >
Vector	m_lower_bound
Vector	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 Vector, typename DerivedSolver>
requires TypeTrait<Vector>::IsEigen && (!TypeTrait<Vector>::IsFixed || TypeTrait<Vector>::Dimension > 0)
class Optimist::RootFinder::QuasiNewton< Vector, DerivedSolver >

Quasi-Newton method

The quasi-Newton is a family of methods that approximate the Jacobian matrix or its inverse. Such methods are based on the linearization of the function \(\mathbf{f}(\mathbf{x})\) around the current iterate \(\mathbf{x}_k\), which leads to the linear system

\[ \mathbf{Jf}_{\mathbf{x}}(\mathbf{x}_k) \mathbf{h}_k = -\mathbf{f}(\mathbf{x}_k) \text{.} \]

Here, the Jacobian matrix \(\mathbf{Jf}_{\mathbf{x}}\) is supposed not to be explicitly available or computationally expensive to compute. For this reason, quasi-Newton methods approximate it iteratively.

Template Parameters

Vector	Eigen vector type.
DerivedSolver	Derived solver type.

Member Typedef Documentation

◆ Scalar

template<typename Vector, typename DerivedSolver>

using Optimist::RootFinder::QuasiNewton< Vector, DerivedSolver >::Scalar = typename TypeTrait<Vector>::Scalar

◆ VectorTrait

template<typename Vector, typename DerivedSolver>

using Optimist::RootFinder::QuasiNewton< Vector, DerivedSolver >::VectorTrait = TypeTrait<Vector>

Constructor & Destructor Documentation

◆ QuasiNewton()

template<typename Vector, typename DerivedSolver>

Optimist::RootFinder::QuasiNewton< Vector, DerivedSolver >::QuasiNewton ( )

inline

Class constructor for the QuasiNewton solver.

Member Function Documentation

◆ name_impl()

template<typename Vector, typename DerivedSolver>

std::string Optimist::RootFinder::QuasiNewton< Vector, DerivedSolver >::name_impl ( ) const

inlineconstexpr

Get the QuasiNewton solver name.

Returns: The QuasiNewton solver name.

◆ solve_impl()

template<typename Vector, typename DerivedSolver>

template<typename FunctionLambda, typename JacobianLambda>

bool Optimist::RootFinder::QuasiNewton< Vector, DerivedSolver >::solve_impl	(	FunctionLambda &&	function,
		JacobianLambda &&	jacobian,
		const Vector &	x_ini,
		Vector &	x_sol )

inline

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

Template Parameters

FunctionLambda	Function lambda type.
JacobianLambda	Jacobian lambda type.

Parameters

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

Returns: The convergence boolean flag.

◆ update()

template<typename Vector, typename DerivedSolver>

void Optimist::RootFinder::QuasiNewton< Vector, DerivedSolver >::update	(	const Vector &	delta_x_old,
		const Vector &	delta_function_old,
		const FirstDerivative &	jacobian_old,
		const Vector &	delta_x_new,
		const Vector &	delta_function_new,
		const Vector &	function_new,
		FirstDerivative &	jacobian_new )

inline

Jacobian approximation update rule for the QuasiNewton's method.

Parameters

[in]	delta_x_old	Old difference between points.
[in]	delta_function_old	Old difference between function values.
[in]	jacobian_old	Old jacobian approximation.
[in]	delta_x_new	New difference between points.
[in]	delta_function_new	New difference between function values.
[in]	function_new	New function value.
[out]	jacobian_new	New jacobian approximation.

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

core/include/Optimist/RootFinder/QuasiNewton.hh

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Quasi-Newton method

Member Typedef Documentation

◆ Scalar

◆ VectorTrait

Constructor & Destructor Documentation

◆ QuasiNewton()

Member Function Documentation

◆ name_impl()

◆ solve_impl()

◆ update()