[Quantlib-dev] optimizers

[Bianchetti M. <mar...@ca...>]

Hello,
=20
at the moment are available into QuantLib the following optimizers:

*	Simplex (recently revisited: the Numerical Recipes
implementation badly failed in finding the minimum of a 1D parabole...)
*	Levenberg-Marquardt
*	Conjugate Gradient
*	Steepest Descent (still to be debugged, work in progress)

and we are currently considering the option to port into QuantLib the
Broyden-Fletcher-Goldfarb-Shanno (BFGS2) algorithm, which in GSL is
declared to be the best (see the text below). So:

*	Any comment on the choice of BFGS2? do anyone has experience
with it ?
*	is anyone aware of an available open source C++ implementation
to be ported into Quantlib with small effort ?

Personally, I would prefer NOT to translate the GSL implementation from
C to C++, because of the danger to introduce some tricky bug and because
it requires a much more sophisticated test suite (and much work).
=20
ciao
Marco
=20
---
from:
http://www.gnu.org/software/gsl/manual/html_node/Multimin-Algorithms.htm
l
Minimizer: gsl_multimin_fdfminimizer_vector_bfgs2
Minimizer: gsl_multimin_fdfminimizer_vector_bfgs


	These methods use the vector Broyden-Fletcher-Goldfarb-Shanno
(BFGS) algorithm. This is a quasi-Newton method which builds up an
approximation to the second derivatives of the function f using the
difference between successive gradient vectors. By combining the first
and second derivatives the algorithm is able to take Newton-type steps
towards the function minimum, assuming quadratic behavior in that
region.=20

	The bfgs2 version of this minimizer is the most efficient
version available, and is a faithful implementation of the line
minimization scheme described in Fletcher's Practical Methods of
Optimization, Algorithms 2.6.2 and 2.6.4. It supercedes the original
bfgs routine and requires substantially fewer function and gradient
evaluations. The user-supplied tolerance tol corresponds to the
parameter \sigma used by Fletcher. A value of 0.1 is recommended for
typical use (larger values correspond to less accurate line searches).=20