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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)


  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



  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


 '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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