NAME
Algorithm::LBFGS - Perl extension for L-BFGS
SYNOPSIS
use Algorithm::LBFGS;
# f(x) = x^2
sub f() {
my $x = shift;
return $x->[0] * $x->[0];
}
# grad f(x) = 2x
sub g() {
my $x = shift;
return [ 2 * $x->[0] ];
}
# minimize
my $xt = fmin($f, $g, [5]); # $xt = [0]
DESCRIPTION
L-BFGS is a limited-memory quasi-Newton method for unconstrained optimization. This method is especially efficient on problems involving a large number of variables.
It solves a problem described as following:
min f(x), x = (x1, x2, ..., xn)
This module is a Perl port of its Fortran 77 version by Jorge Nocedal.
http://www.ece.northwestern.edu/~nocedal/lbfgs.html
fmin
fmin(f, g, x0)
finds a vector x
which minimize the function f(x)
.
f
- The reference to thef(x)
function. This function is supposed to accept an array reference (the vector ofx
) and return a scalar (the valuef(x)
).g
- The reference to thegrad f(x)
function (grad
for gradient). This function is supposed to accept an array reference (the vectorx
) and return an array reference (the gradient vector atf(x)
).x0
- The initial value ofx
. It is supposed to be an array reference.
fmin
returns the optimized x
on success, otherwise returns undef
.
$Algorithm::LBFGS::m
m
is an positive integer value that can be set by the user to the number of corrections used in the BFGS update. Values of m
less than 3 are not recommended; large values of m
will result in excessive computing time. 3 <= m >= 7
is recommended. The default value of m
is 5.
$Algorithm::LBFGS::xtol
xtol
is a positive value that can be set by the user to an estimate of the machine precision. The line search routine will terminate if the relative width of the interval of uncertainty is less than xtol
. The default value of xtol
is equal to the DBL_EPSILON
in float.h.
$Algorithm::LBFGS::eps
eps
is a positive DOUBLE value that can be set by the user to determine the accuracy with which the solution is to be found. The subroutine terminates when
||G|| < eps max(1,||X||)
where ||.||
denotes the Euclidean norm. The default value of eps
is equal to the DBL_EPSILON
in float.h.
$Algorithm::LBFGS::gtol
gtol
is a value with default value 0.9, which controls the accuracy of the line search. If the f(x)
and grad f(x)
evaluations are inexpensive with respect to the cost of the iteration (which is sometimes the case when solving very large problems) it may be advantageous to set gtol
to a small value. A typical small value is 0.1. gtol
should be greater than 1E-04.
$Algorithm::LBFGS::stpmin and $Algorithm::LBFGS::stpmax
stpmin
and stpmax
are non-negative value which specify lower and upper bounds for the step in the line search. Their default values are 1.D-20 and 1.D+20, respectively. These values need not be modified unless the exponents are too large for the machine being used, or unless the problem is extremely badly scaled (in which case the exponents should be increased).
$Algorithm::LBFGS::iprt1 and $Algorithm::LBFGS::iprt2
iprt1
and iprt2
can be specified to control the output.
iprt1
specifies the frequency of the output:
iprt1 < 0
: no output is generated,iprt1 = 0
: output only at first and last iteration,iprt1 > 0
: output every iterations.
iprt2
specifies the type of output generated:
iprt2 = 0
: iteration count, number of function evaluations, function value, norm of the gradient, and steplength,iprt2 = 1
: same asiprt2 = 0
, plus vector of variables and gradient vector at the initial point,iprt2 = 2
: same asiprt2 = 1
, plus vector of variables,iprt2 = 3
: same asiprt2 = 2
, plus gradient vector.
The default value of iprt1
and iprt2
is 1, 0 respectively.
DEPENDENCY
To build the module, you need to install libf2c
beforehand.
SEE ALSO
AUTHOR
Laye Suen, <laye@cpan.org>
COPYRIGHT AND LICENSE
Copyright (C) 2008 by Laye Suen
This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.8.8 or, at your option, any later version of Perl 5 you may have available.