Re: [Quantlib-dev] optimizers

[DU V. DE V. F. G. P. <fra...@ca...>]

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Here is a good C++ implementation candidate,=20

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http://www.alglib.net/optimization/lbfgs.php

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Though, I'm not absolutely sure that the terms of use are compatible =
with those of QL.=20

Fran=E7ois

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-----Original Message-----
From: qua...@li... =
[mailto:qua...@li...] On Behalf Of =
Bianchetti Marco
Sent: Wednesday, May 23, 2007 6:13 PM
To: qua...@li...
Subject: [Quantlib-dev] optimizers

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Hello,

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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).

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ciao

Marco

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---

from: =
http://www.gnu.org/software/gsl/manual/html_node/Multimin-Algorithms.html=


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