minimization using the Brent algorithm (brent.c)

Fabrice Rossi rossi@ufrmd.dauphine.fr
Mon Mar 17 22:03:00 GMT 2003


Stated like this, I mostly agree with you, except maybe on vocabulary. 
What is called the Brent algorithm or the Golden section search is 
exactly what is (currently) implemented in GSL. But as Michael and you 
pointed out, in practical situation, we need a way to start the 
algorithm. The rationnal why this is not included into GSL (well, it 
once was in my first implementation of multidimensional minimization) is 
(to my mind) that it is highly problem dependant. Nevertheless, this 
discussion seems to show that a general solution (maybe suboptimal) is 
needed.

By the way a simple example why this is problem dependant: take 
multidimensional minimization. In general, you have to perform a line 
search at each step. As you want something fully automated, in some 
cases you have to provide the now famous middle point! For instance, 
when you are working with conjugate gradient algorithms, you must have a 
correct (not very precise, but still correct) estimation of the minimum 
in the line search. It is a good idea to rely on the Brent algorithm to 
do this line search, but as you have evaluated the gradient at the 
starting point, you can use this information to find the middle point 
more efficiently that you would do in the general case (in which you 
cannot assume knowledge of the derivative). Moreover, in some particular 
applications (for instance neural networks) and under particular 
circonstances, you can even more tune your algorithm, for instance be 
reusing results from previous line searches.

Fabrice Rossi



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