Re: multidimensional optimization

[Brian Gough <bjg at network-theory dot co dot uk>]

Fabrice Rossi writes:
 >  - parameters:
 >  Is it better to have a big structure that discribes the parameters
 > of the one dimensional part (as that is going to be contained in
 > the gsl_min_fX_G_minimizer structure that contains the base state
 > of the descent algorithm), or to pass these parameters to the
 > iterate function (that runs one iteration of the descent
 > algorithm)?

It might be important for the user to follow the progress of the 1d
minimisations, so perhaps the algorithm should be split twice. A
separate inner loop for the 1-d minimisation could be used like this,

    do {
      get gradient
      do {
        minimise in 1d
      } while (!converged_1d)
      ...
   } while (!converged)

I'm don't think that the user should call the existing gsl_min
functions --- we would provide a suitable minimisation function (maybe
a wrapper around an existing gsl_min function) that will take care of
the vector arithmetic so the 1d minimisation is as simple as the outer
loop.

 >  - iteration:
 >  If I focus on descent algorithms, I think that I don't need a
 > different iterate function for each algorithm, basically because
 > the only think that really differs between two such algorithms is
 > the way the descent direction is calculated. So I think it's better
 > to have a direction function that computes a new descent
 > direction. I don't know any algorithm that need something else than
 > the value of the function and of its gradient at the current
 > estimate of the minimum and previous descent directions. I guess
 > that I don't need to provide the function itself to the algorithm
 > as long as I give it the current gradient and value. Any objection?

No objection. If there is a more natural way to decompose the algorithm
then it is better to use that.