Algorithm-LBFGS
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the initial point of the optimization algorithm, "progress_cb"
(optional) is a ref to the progress callback subroutine, and "user_data"
(optional) is a piece of extra data that client program want to pass to
both "evaluation_cb" and "progress_cb".
Client program can use "get_status" to find if any problem occured
during the optimization after their calling "fmin". When the status is
"LBFGS_OK", the returning value "x" (array ref) contains the optimized
variables, otherwise, there may be some problems occured and the value
in the returning "x" is undefined.
evaluation_cb
The ref to the evaluation callback subroutine.
The evaluation callback subroutine is supposed to calculate the function
value and gradient vector at a specified point "x". It is called
automatically by "fmin" when an evaluation is needed.
The client program need to make sure their evaluation callback
subroutine has a prototype like
(f, g) = evaluation_cb(x, step, user_data)
"x" (array ref) is the current values of variables, "step" is the
current step of the line search routine, "user_data" is the extra user
data specified when calling "fmin".
The evaluation callback subroutine is supposed to return both the
function value "f" and the gradient vector "g" (array ref) at current
"x".
x0
The initial point of the optimization algorithm. The final result may
depend on your choice of "x0".
NOTE: The content of "x0" will be modified after calling "fmin". When
the algorithm terminates successfully, the content of "x0" will be
replaced by the optimized variables, otherwise, the content of "x0" is
undefined.
progress_cb
The ref to the progress callback subroutine.
The progress callback subroutine is called by "fmin" at the end of each
iteration, with information of current iteration. It is very useful for
a client program to monitor the optimization progress.
The client program need to make sure their progress callback subroutine
has a prototype like
s = progress_cb(x, g, fx, xnorm, gnorm, step, k, ls, user_data)
"x" (array ref) is the current values of variables. "g" (array ref) is
the current gradient vector. "fx" is the current function value. "xnorm"
and "gnorm" is the L2 norm of "x" and "g". "step" is the line-search
step used for this iteration. "k" is the iteration count. "ls" is the
number of evaluations in this iteration. "user_data" is the extra user
data specified when calling "fmin".
The progress callback subroutine is supposed to return an indicating
value "s" for "fmin" to decide whether the optimization should continue
or stop. "fmin" continues to the next iteration when "s=0", otherwise,
it terminates with status code "LBFGSERR_CANCELED".
The client program can also pass string values to "progress_cb", which
means it want to use a predefined progress callback subroutine. There
are two predefined progress callback subroutines, 'verbose' and
'logging'. 'verbose' just prints out all information of each iteration,
while 'logging' logs the same information in an array ref provided by
"user_data".
...
# print out the iterations
fmin($eval_cb, $x0, 'verbose');
# log iterations information in the array ref $log
my $log = [];
fmin($eval_cb, $x0, 'logging', $log);
use Data::Dumper;
print Dumper $log;
user_data
The extra user data. It will be sent to both "evaluation_cb" and
"progress_cb".
get_status
Get the status of previous call of "fmin".
...
$o->fmin(...);
# check the status
if ($o->get_status eq 'LBFGS_OK') {
...
}
# print the status out
print $o->get_status;
The status code is a string, which could be one of those in the "List of
Status Codes".
status_ok
This is a shortcut of saying "get_status" eq "LBFGS_OK".
...
if ($o->fmin(...), $o->status_ok) {
...
}
List of Parameters
m
The number of corrections to approximate the inverse hessian matrix.
The L-BFGS algorithm stores the computation results of previous "m"
iterations to approximate the inverse hessian matrix of the current
iteration. This parameter controls the size of the limited memories
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