Backtracking line search using the armijo rule. More...

#include <line_search.h>

Inheritance diagram for dismec::solvers::BacktrackingLineSearch:

Public Member Functions
	BacktrackingLineSearch ()

double	get_initial_step () const

void	set_initial_step (double s)
	sets the initial step multiplied. Throws `std::invalid_argument` if `s` is not positive. More...

double	get_alpha () const

void	set_alpha (double a)
	sets the alpha parameter. Throws `std::invalid_argument` if `a` is not in `(0, 1)` More...

double	get_eta () const

void	set_eta (double e)
	sets the eta parameter. Throws `std::invalid_argument` if `e` is not in `(0, 1)` More...

long	get_max_steps () const

void	set_max_steps (long n)
	sets the eta parameter. Throws `std::invalid_argument` if `n` is not positive More...

sLineSearchResult	search (const std::function< double(double)> &projected_objective, double gTs, double f_init) const

Public Member Functions inherited from dismec::HyperParameterBase
	HyperParameterBase ()=default

virtual	~HyperParameterBase ()=default

	HyperParameterBase (const HyperParameterBase &)=default

	HyperParameterBase (HyperParameterBase &&)=default

HyperParameterBase &	operator= (HyperParameterBase &&)=default

HyperParameterBase &	operator= (const HyperParameterBase &)=default

void	set_hyper_parameter (const std::string &name, long value)

void	set_hyper_parameter (const std::string &name, double value)

hyper_param_t	get_hyper_parameter (const std::string &name) const

std::vector< std::string >	get_hyper_parameter_names () const
	Returns a vector that lists all hyper parameter names. More...

Private Attributes
double	m_StepSize = 1.0

double	m_Alpha = 0.5

double	m_Eta = 0.01

long	m_MaxSteps = 20

Additional Inherited Members
Public Types inherited from dismec::HyperParameterBase
using	hyper_param_t = std::variant< long, double >

Protected Member Functions inherited from dismec::HyperParameterBase
template<class U , class S >
void	declare_hyper_parameter (std::string name, U S::*pointer)

template<class U , class S >
void	declare_hyper_parameter (std::string name, U(S::getter)() const, void(S::setter)(U))
	Declares an constrained hyper-parameter with explicit getter and setter function. More...

template<class T , class S >
void	declare_sub_object (const std::string &name, T S::*object)
	Declares a sub-object that also contains hyper-parameters. More...

Detailed Description

Backtracking line search using the armijo rule.

The algorithm starts with a step size of initial_step (default: 1) times the direction vector. If the reduction of function value is not at least eta (default 0.01) times the expected reduction according to the gradient (i.e. the linear approximation) a step that is smaller by a factor of alpha (default 0.5) is tried. This is repeated until the maximum number of steps has been reached (default: 20). If no adequate point is found then, a step of 0 is returned.

This class gets supplied with a "projected objective", i.e. an objective function g: R->R that is related to the original as follows: g(a) = f(x_0 + a d) where d is the search direction and x_0 is the starting point.

Definition at line 35 of file line_search.h.

Constructor & Destructor Documentation

◆ BacktrackingLineSearch()

BacktrackingLineSearch::BacktrackingLineSearch ( )

Definition at line 13 of file line_search.cpp.

References dismec::HyperParameterBase::declare_hyper_parameter(), get_alpha(), get_eta(), get_initial_step(), get_max_steps(), set_alpha(), set_eta(), set_initial_step(), and set_max_steps().

Member Function Documentation

◆ get_alpha()

double dismec::solvers::BacktrackingLineSearch::get_alpha ( ) const

inline

Definition at line 44 of file line_search.h.

References m_Alpha.

Referenced by BacktrackingLineSearch().

◆ get_eta()

double dismec::solvers::BacktrackingLineSearch::get_eta ( ) const

inline

Definition at line 48 of file line_search.h.

References m_Eta.

Referenced by BacktrackingLineSearch().

◆ get_initial_step()

double dismec::solvers::BacktrackingLineSearch::get_initial_step ( ) const

inline

Definition at line 40 of file line_search.h.

References m_StepSize.

Referenced by BacktrackingLineSearch().

◆ get_max_steps()

long dismec::solvers::BacktrackingLineSearch::get_max_steps ( ) const

inline

Definition at line 52 of file line_search.h.

References m_MaxSteps.

Referenced by BacktrackingLineSearch().

◆ search()

sLineSearchResult BacktrackingLineSearch::search	(	const std::function< double(double)> &	projected_objective,
		double	gTs,
		double	f_init
	)		const

Parameters

projected_objective	A function that when called with parameter \( \alpha \) , will return the value of the objective along the search direction \(d\) given by \( g(\alpha) = f(x_0 + \alpha d) \).
gTs	Gradient at 0, i.e. \( \left. \frac{\partial g}{\partial \alpha}\right\|_{\alpha=0}\).
f_init	\( g(0) = f(x_0) \).

Definition at line 20 of file line_search.cpp.

References m_Alpha, m_Eta, m_MaxSteps, and m_StepSize.

Referenced by dismec::solvers::NewtonWithLineSearch::run().