[SciPy-dev] Brent's Principal Axis Algorithm

[Robert Kern]

On Tue, Sep 8, 2009 at 12:44, Christoph
Schmidt-Hieber<c.schmidt-hieber at ucl.ac.uk> wrote:
> Dear all,
> I've started a Google code project (http://code.google.com/p/pypraxis/) to provide a Python interface to Brent's principal axis algorithm. It's basically a wrapper around some Fortran code from http://www.netlib.org/opt/. Brent's algorithm minimizes a function of several variables without calculating derivatives - not to be mistaken for scipy.optimize.brent, that only performs single-variable minimization. The algorithm typically outperforms other derivative- and gradient-free algorithms (Brent, 2002; http://wwwmaths.anu.edu.au/~brent/pub/pub011.html). In my experience, it converges substantially faster than fmin and fmin_powell from scipy.optimize when fitting models with 5 to 15 free parameters to experimental data. Notably, Mathematica uses this algorithm for minimization without derivatives
> (http://reference.wolfram.com/mathematica/tutorial/UnconstrainedOptimizationPrincipalAxisMethod.html).
> I've provided some test cases and a wrapper that allow to compare it directly to the existing algorithms from scipy.optimize. Let me know if you think that the code could be a candidate for integration into scipy.optimize. It would obviously require some work to make it conform with the other functions that are already present.

That would be great! Unfortunately, there is no license attached to
praxis.f, so it cannot be integrated into scipy until we find a
suitably licensed implementation of the algorithm.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
  -- Umberto Eco