Armijo line search. More...

#include <ql/math/optimization/armijo.hpp>

Inheritance diagram for ArmijoLineSearch:

Collaboration diagram for ArmijoLineSearch:

Public Member Functions
	ArmijoLineSearch (Real eps=1e-8, Real alpha=0.05, Real beta=0.65)
	Default constructor. More...

Real	operator() (Problem &P, EndCriteria::Type &ecType, const EndCriteria &, Real t_ini) override
	Perform line search. More...

Public Member Functions inherited from LineSearch
	LineSearch (Real=0.0)
	Default constructor. More...

virtual	~LineSearch ()=default
	Destructor. More...

const Array &	lastX ()
	return last x value More...

Real	lastFunctionValue () const
	return last cost function value More...

const Array &	lastGradient ()
	return last gradient More...

Real	lastGradientNorm2 () const
	return square norm of last gradient More...

bool	succeed () const

virtual Real	operator() (Problem &P, EndCriteria::Type &ecType, const EndCriteria &, Real t_ini)=0
	Perform line search. More...

Real	update (Array &params, const Array &direction, Real beta, const Constraint &constraint)

const Array &	searchDirection () const
	current value of the search direction More...

Array &	searchDirection ()

Private Attributes
Real	alpha_

Real	beta_

Additional Inherited Members
Protected Attributes inherited from LineSearch
Array	searchDirection_
	current values of the search direction More...

Array	xtd_
	new x and its gradient More...

Array	gradient_

Real	qt_ = 0.0
	cost function value and gradient norm corresponding to xtd_ More...

Real	qpt_ = 0.0

bool	succeed_ = true
	flag to know if linesearch succeed More...

Detailed Description

Armijo line search.

Let \( \alpha \) and \( \beta \) be 2 scalars in \( [0,1] \). Let \( x \) be the current value of the unknown, \( d \) the search direction and \( t \) the step. Let \( f \) be the function to minimize. The line search stops when \( t \) verifies

\[ f(x + t \cdot d) - f(x) \leq -\alpha t f'(x+t \cdot d) \]

and

\[ f(x+\frac{t}{\beta} \cdot d) - f(x) > -\frac{\alpha}{\beta} t f'(x+t \cdot d) \]

(see Polak, Algorithms and consistent approximations, Optimization, volume 124 of Applied Mathematical Sciences, Springer-Verlag, NY, 1997)

Definition at line 48 of file armijo.hpp.

Constructor & Destructor Documentation

◆ ArmijoLineSearch()

ArmijoLineSearch	(	Real	eps = `1e-8`,
		Real	alpha = `0.05`,
		Real	beta = `0.65`
	)

Default constructor.

Definition at line 51 of file armijo.hpp.

Member Function Documentation

◆ operator()()

Real operator()	(	Problem &	P,
		EndCriteria::Type &	ecType,
		const EndCriteria &	endCriteria,
		Real	t_ini
	)

overridevirtual

Perform line search.

Implements LineSearch.

Definition at line 26 of file armijo.cpp.

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Member Data Documentation

◆ alpha_

Real alpha_

private

Definition at line 62 of file armijo.hpp.

◆ beta_

Real beta_