# minimization using the Brent algorithm (brent.c)

Z F mail4me9999@yahoo.com
Mon Mar 17 18:22:00 GMT 2003

```Hello Brian

Sorry for my rudness, but I think that it is not prudent to require
a "test" point inside the interval. (I know that standard libraries
require that). The test F(a)>F(x)<F(b) is a protection againts a
"stupid" mistake, nothing more. It does not guarantee that there is no
point y between a and b that F(y)>F(a) or F(y)>F(b) so the test is
useless and only requires an extra computation of F() which might be
time consuming.

By the way, concering general methods, there is a method which is
faster than the golden section. It is not discussed anywhere in the
"modern" literature, but it exists. This method is not an itterative
one and given the required root accuracy a sequence of test points
is constructed in the extremum search. It was also shown (if I am not
mistaken) that if there is no other knowledge regarding F(x) other then

its values at any X, the method is the fastest. The approch to this
method is completly different from the current GSL thinking.(There are
no itterations, so in some sence it even contradicts the GSL philosophy
on the problem). Thus, if there is a desire to implement this method it
will require some extra work. (Of course, it is possible that I do not
understand the GSL logic accurately.)

Well, just some thoughts...

Lazar

--- Brian Gough <bjg@network-theory.co.uk> wrote:
> Faheem Mitha writes:
>  > I need to use a one-dimensional global minimization algorithm (to
> minimize
>  > a function on an interval). However, this algorithm is embedded
> inside a
>  > larger framework, and needs to be called many times without user
>  > intervention. I discovered that an implementation of this
> algorithm was in
>  > GSL, so I decided to use it.
>  >
>
> The GSL minimization routines are designed for finding a guaranteed
> bound on a local minimum f(a)>f(x)<f(b).  They don't cover the case
> of
> a minimum occuring at an endpoint.
>
> If you want to make use of the brent algorithm, you could copy it
> from
> GSL into your own program, rather than modifying the library itself.
>
> regards,
> --
> Brian Gough
>
>
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