Multidimensional minimization by the BFGS algorithm (GSL) More...

#include <mmin_bfgs2.h>

Inheritance diagram for o2scl::mmin_bfgs2< func_t, vec_t, dfunc_t, auto_grad_t, def_auto_grad_t >:

Detailed Description

template<class func_t = multi_funct, class vec_t = boost::numeric::ublas::vector<double>, class dfunc_t = grad_funct, class auto_grad_t = gradient<multi_funct,boost::numeric::ublas::vector<double> >, class def_auto_grad_t = gradient_gsl<multi_funct,boost::numeric::ublas::vector<double> >>
class o2scl::mmin_bfgs2< func_t, vec_t, dfunc_t, auto_grad_t, def_auto_grad_t >

The functions mmin() and mmin_de() min a given function until the gradient is smaller than the value of mmin::tol_rel (which defaults to $10^{-4}$ ).

See an example for the usage of this class in Multidimensional minimizer example .

This class includes the optimizations from the GSL minimizer vector_bfgs2.

Default template arguments

func_t - multi_funct
vec_t - boost::numeric::ublas::vector <double >
dfunc_t - mm_funct
auto_grad_t - gradient<func_t, boost::numeric::ublas::vector <double > >
def_auto_grad_t - gradient_gsl<func_t, boost::numeric::ublas::vector < double > >

Todo:
While BFGS does well in the ex_mmin example with the initial guess of $(1,0,7\pi)$ it seems to converge more poorly for the spring function than the other minimizers with other initial guesses, and I think this will happen in the GSL versions too. I need to examine this more closely with some code designed to clearly show this.

Idea for Future:
When the bfgs2 line minimizer returns a zero status, the minimization fails. When err_nonconv is false, the minimizer isn't able to update the x vector so the mmin() function doesn't return the best minimum obtained so far. This is a bit confusing, and could be improved.

Definition at line 387 of file mmin_bfgs2.h.

Protected Attributes
The original variables from the GSL state structure
int	iter

double	step

double	g0norm

double	pnorm

double	delta_f

double	fp0

vec_t	x0

vec_t	g0

vec_t	p

vec_t	dx0

vec_t	dg0

mmin_wrapper_gsl< func_t, vec_t, dfunc_t, auto_grad_t >	wrap

double	rho

double	sigma

double	tau1

double	tau2

double	tau3

int	order

mmin_linmin_gsl	lm
	The line minimizer.

Protected Attributes inherited from o2scl::mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > >
std::ostream *	outs
	Stream for verbose output.

std::istream *	ins
	Stream for verbose input.

Store the arguments to set() so we can use them for iterate()
vec_t *	st_x

vec_t	st_dx

vec_t	st_grad

double	st_f

size_t	dim
	Memory size.

auto_grad_t *	agrad
	Automatic gradient object.

double	step_size
	The size of the first trial step (default 0.01)

double	lmin_tol
	The tolerance for the 1-dimensional minimizer.

def_auto_grad_t	def_grad
	Default automatic gradient object.

	mmin_bfgs2 ()

virtual	~mmin_bfgs2 ()

virtual int	iterate ()
	Perform an iteration.

virtual const char *	type ()
	Return string denoting type("mmin_bfgs2")

virtual int	allocate (size_t n)
	Allocate the memory.

virtual int	free ()
	Free the allocated memory.

int	restart ()
	Reset the minimizer to use the current point as a new starting point.

virtual int	set (vec_t &x, double u_step_size, double tol_u, func_t &ufunc)
	Set the function and initial guess.

virtual int	set_de (vec_t &x, double u_step_size, double tol_u, func_t &ufunc, dfunc_t &udfunc)
	Set the function, the gradient, and the initial guess.

virtual int	mmin (size_t nn, vec_t &xx, double &fmin, func_t &ufunc)
	Calculate the minimum `min` of `func` w.r.t the array `x` of size `nn`.

virtual int	mmin_de (size_t nn, vec_t &xx, double &fmin, func_t &ufunc, dfunc_t &udfunc)
	Calculate the minimum `min` of `func` w.r.t the array `x` of size `nn`.

	mmin_bfgs2 (const mmin_bfgs2< func_t, vec_t, dfunc_t, auto_grad_t, def_auto_grad_t > &)

mmin_bfgs2< func_t, vec_t, dfunc_t, auto_grad_t, def_auto_grad_t > &	operator= (const mmin_bfgs2< func_t, vec_t, dfunc_t, auto_grad_t, def_auto_grad_t > &)

Additional Inherited Members
Public Member Functions inherited from o2scl::mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > >
	mmin_base (const mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > > &mb)
	Copy constructor.

int	set_verbose_stream (std::ostream &out, std::istream &in)
	Set streams for verbose I/O. More...

virtual int	mmin (size_t nvar, boost::numeric::ublas::vector< double > &x, double &fmin, multi_funct &func)=0
	Calculate the minimum `min` of `func` w.r.t. the array `x` of size `nvar`.

virtual int	mmin_de (size_t nvar, boost::numeric::ublas::vector< double > &x, double &fmin, multi_funct &func, multi_funct &dfunc)
	Calculate the minimum `min` of `func` w.r.t. the array `x` of size `nvar` with gradient `dfunc`.

int	print_iter (size_t nv, vec2_t &x, double y, int iter, double value, double limit, std::string comment)
	Print out iteration information. More...

const char *	type ()
	Return string denoting type ("mmin_base")

mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > > &	operator= (const mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > > &mb)
	Copy constructor from operator=.

Public Attributes inherited from o2scl::mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > >
int	verbose
	Output control.

int	ntrial
	Maximum number of iterations.

double	tol_rel
	Function value tolerance.

double	tol_abs
	The independent variable tolerance.

int	last_ntrial
	The number of iterations for in the most recent minimization.

bool	err_nonconv
	If true, call the error handler if the routine does not "converge".

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

/home/awsteiner/wcs/o2scl/src/min/mmin_bfgs2.h

Detailed Description

Protected Attributes

Store the arguments to set() so we can use them for iterate()

Additional Inherited Members