Help: working with large gsl_vector

[Fabrice Rossi]

Toan T Nguyen wrote:
> I'm using the multidimensional minimization procedure in GSL and have problem 
> with large vectors. The dimensionality of my vectors is 300000 which means my 
> index variable is of long integer type. 

Hum. I authored the initial version of the multidimensional minimization 
functions which have been improved by others, but I don't think they 
have been improved in such a way that optimization in dimension 300 000 
is possible. Even for a quadratic function and using a conjugate 
gradient algorithm, it will take 3e5 iterations to the algorithm to 
complete. As each iteration implies a linear search for minimum that 
will use at least around 10 evaluations of your function, your a looking 
for 3e6 function evaluation. Unless you have a very special problem, I 
would guess that a function evaluation take at least 3e5 operations to 
complete, which implies 9e11 operations (a.k.a. 2^39 operations). That's 
a lot. And we are talking about a quadratic form, remember ?

Perhaps you could tell us a little bit more about your application ?

Fabrice

PS : Support Vector Machine algorithms have proven that it is indeed 
possible to do quadratic optimization under constraints in high 
dimensional space (like 10000 dimensions), but they use _very_ complex 
methods.