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## Function minimzation functions

 From: Etienne Grossmann Subject: Function minimzation functions Date: Mon, 16 Oct 2000 20:56:39 +0100 User-agent: WEMI/1.13.7 (Shimada) FLIM/1.13.2 (Kasanui) Emacs/20.7 (i386-debian-linux-gnu) (with unibyte mode)

```  Hello,

just to say that I have put a conjugate gradient and a
Davidon-Fletcher-Powell method for optimization of functions whose
derivatives are available.

I am not very happy with the Synopsis, so I might change it in the
future.

Cheers,

Etienne

The Synopsis for DFP goes like this :

======================================================================

[x,v,niter,h] = dfp_min(func,dfunc,xinit,options)

Broyden-Fletcher-Goldfarb-Shanno Variable metric method for
minimizing the function 'func', whose derivative is 'dfunc', starting
from 'xinit'.

TODO : Ease the following restrictions

- xinit is a N-by-1 column vector.
- func  takes a single (column vector) argument.
- dfunc takes a single (column vector) argument and returns a row
vector.

OPTIONS

'vinit',v     : Value of the function at the starting xinit.
'maxiter', m  : At most m iterations are done (default : 200)
'gtol',gtol   : Set the threshold for the stopping criterion

gtol > max { df(i)*max(|x(i)|,1)/max(v,1) | i in 1..N }

where x is the current minimum, v is func(x) and df
is dfunc(x).
Default value is 10*eps

'tol', tol    : Set the threshold for the stopping criterion

tol > max { dx(i)/max(|x(i)|,1) | i in 1..N }

where  dx is the change in the x that occured in the
last iteration.
Default value is 10*eps

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```