algo::qn::BroydenFletcherGoldfarbShanno< T > Class Template Reference

Inheritance diagram for algo::qn::BroydenFletcherGoldfarbShanno< T >:

Public Types
typedef std::function< T(const ublas::vector< T > &x)>	function_type
Public Types inherited from algo::qn::IQuasiNewton< T >
typedef std::function< T(const ublas::vector< T > &x)>	function_type

Public Member Functions
	BroydenFletcherGoldfarbShanno (const double epsilon, const std::size_t maxIteration)
Public Member Functions inherited from algo::qn::IQuasiNewton< T >
ublas::vector< double >	operator() (const ublas::vector< double > &x0, const function_type &f, const std::shared_ptr< ILineSearcher > searcher)
	solve $\mathrm{argmin}_{x}f(x) More...
Public Member Functions inherited from util::Object< IQuasiNewton< T > >
const IQuasiNewton< T > &	cast ()
bool	operator== (const IQuasiNewton< T > &o) const
std::shared_ptr< IQuasiNewton< T > >	clone () const

Private Member Functions
ublas::vector< double >	doOperatorParenthesis (const ublas::vector< double > &x0, const function_type &f, const std::shared_ptr< ILineSearcher > searcher)
ublas::matrix< double >	calculateInverseHessian (const ublas::vector< double > &x1, const ublas::vector< double > &x2, const ublas::vector< double > &df1, const ublas::vector< double > &df2, const ublas::matrix< double > &H)
	calculates inverse hessian by follwoing formula: $$ B_{k+1}^{-1} := \left(I - \frac{dx_{k} y_{k}^{T}}{y_{k}^{T}dx_{k}} \right) B_{k}^{-1} \left( I - \frac{y_{k}dx_{k}^{T}}{y_{k}^{T}dx_{k}}\right) + \frac{dx_{k}dx^{T}}{y_{k}^{T}s_{k}}. $$ Here $B_{k}$ is $k$-th hessian, $dx_{k} := x_{k+1} - x_{k}$, $I$ is identity matrix, $y_{k} := df_{k+1} - df_{k}.$ Following formula is derived from above equation. $$ B_{k+1}^{-1} = \frac{B_{k}^{-1} + (dx_{k}^{T}y_{k} + y_{k}^{T}B_{k}^{-1}y_{k})(dx_{k}dx_{k}^{T})}{(dx_{k}^{T}y_{k})^{2}} - \frac{B_{k}^{-1}y_{k}dx_{k}^{T} + dx_{k}y_{k}^{T}B_{k}^{-1}}{dx_{k}^{T}y_{k}}. $$ More...
bool	isConverge (const ublas::vector< double > &x1, const ublas::vector< double > &x2)
	Check whether algorithm is converged or not. More...

Private Attributes
const double	_epsilon
const std::size_t	_maxIteration

Constructor & Destructor Documentation

template<typename T >

template algo::qn::BroydenFletcherGoldfarbShanno< T >::BroydenFletcherGoldfarbShanno	(	const double	epsilon,
		const std::size_t	maxIteration
	)

Parameters

epsilon	algorithm is converged if error is less than epsilon.
maxIteration	algorithm is iterated until converged or number of maxInteration.

Member Function Documentation

template<typename T >

template ublas::matrix< double > algo::qn::BroydenFletcherGoldfarbShanno< T >::calculateInverseHessian ( const ublas::vector< double > &  x1, const ublas::vector< double > &  x2, const ublas::vector< double > &  df1, const ublas::vector< double > &  df2, const ublas::matrix< double > &  H  )

private

calculates inverse hessian by follwoing formula: $$ B_{k+1}^{-1} := \left(I - \frac{dx_{k} y_{k}^{T}}{y_{k}^{T}dx_{k}} \right) B_{k}^{-1} \left( I - \frac{y_{k}dx_{k}^{T}}{y_{k}^{T}dx_{k}}\right) + \frac{dx_{k}dx^{T}}{y_{k}^{T}s_{k}}. $$ Here $B_{k}$ is $k$-th hessian, $dx_{k} := x_{k+1} - x_{k}$, $I$ is identity matrix, $y_{k} := df_{k+1} - df_{k}.$ Following formula is derived from above equation. $$ B_{k+1}^{-1} = \frac{B_{k}^{-1} + (dx_{k}^{T}y_{k} + y_{k}^{T}B_{k}^{-1}y_{k})(dx_{k}dx_{k}^{T})}{(dx_{k}^{T}y_{k})^{2}} - \frac{B_{k}^{-1}y_{k}dx_{k}^{T} + dx_{k}y_{k}^{T}B_{k}^{-1}}{dx_{k}^{T}y_{k}}. $$

Todo:

check the first equation is correct or not.

Parameters

x1	previous value.
x2	current value.
df1
df2
H	previous inverse hessian.

Returns

inverse hessian.

template<typename T >

template bool algo::qn::BroydenFletcherGoldfarbShanno< T >::isConverge ( const ublas::vector< double > &  x1, const ublas::vector< double > &  x2  )

private

Check whether algorithm is converged or not.

Parameters

x1	previous value.
x2	current value.

Returns

true if algorithm is converged.

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

• algo/qn/BroydenFletcherGoldfarbShanno.h
• algo/qn/BroydenFletcherGoldfarbShanno.cpp