Re: [ublas] Nonlinear Conjugate Gradient Method

From: Gunter Winkler (guwi17_at_[hidden])
Date: 2006-10-24 14:16:07

Hi Fred and Karl,

Karl Meerbergen schrieb:
> I vaguely recall that conjugate gradients is an optimization method. But I do 
> not recall the details for nonlinear problems. Convergence is only guaranteed 
> for specific math properties, as this is also the case for linear systems.
>   

Yes. Linear CG is a method to find (the unique) vector x that minimizes 
a (scalar) quadratic function

f(x) := 1/2 <x, Ax> - <b, x>  -> min

( <a,b> is any inner product, such that <x, Ax> > 0 for all x<>0 )

Although I must admit that I never heard of "the nonlinear CG". There 
are lots of gradient based methods for nonlinear minimization.

Fred, can you explain your method?

mfg
Gunter