ArmijoLineSearch Class Reference

Armijo line search. More...

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

Inheritance diagram for ArmijoLineSearch:

Public Member Functions
	ArmijoLineSearch (Real eps=1e-8, Real alpha=0.05, Real beta=0.65)
	Default constructor.
Real	operator() (Problem &P, EndCriteria::Type &ecType, const EndCriteria &, const Real t_ini)
	Perform line search.
Public Member Functions inherited from LineSearch
	LineSearch (Real=0.0)
	Default constructor.
virtual	~LineSearch ()
	Destructor.
const Array &	lastX ()
	return last x value
Real	lastFunctionValue ()
	return last cost function value
const Array &	lastGradient ()
	return last gradient
Real	lastGradientNorm2 ()
	return square norm of last gradient
bool	succeed ()
Real	update (Array &params, const Array &direction, Real beta, const Constraint &constraint)
const Array &	searchDirection () const
	current value of the search direction
Array &	searchDirection ()

Additional Inherited Members
Protected Attributes inherited from LineSearch
Array	searchDirection_
	current values of the search direction
Array	xtd_
	new x and its gradient
Array	gradient_
Real	qt_
	cost function value and gradient norm corresponding to xtd_
Real	qpt_
bool	succeed_
	flag to know if linesearch succeed

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)