Re: [ublas] Nonlinear Conjugate Gradient Method

From: James N. Knight (nate_at_[hidden])
Date: 2006-10-24 15:45:16

You can read about Nonlinear cg here: http://tinyurl.com/yd37bt

This thread seems a bit off topic, but before it dies I wanted to say that 
I'm working on a generic nonlinear optimization library that can (and currently does) 
use ublas for the linear algebra representation and algorithms.  The code is generic 
with respect to the function being optimized, the linear algebra facilities, and the 
space being optimized over.  If the original poster or anyone else is interested please
email me offlist.

James

Gunter Winkler wrote:
> 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
> 
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