Re: [Help-gsl] Rationale behind intermediate_point()

[Brian Gough]

At Fri, 08 Oct 2010 12:07:18 -0500,
Johan Hattne wrote:
> While comparing two different implementations of a multidimensional
> optimiser I noticed the backtracking algorithm implemented in
> intermediate_point() in GSL's multimin/directional_minimize.c.  It's not
> obvious to me why the step size is decreased the way it is, i.e.
> 
>   step <- 0.5 * step * u / (df + u)
> 
> where u is the length of the step along the line on which a minimum is
> sought, and df = f(x0 + u) - f(x0).  Could anyone enlighten me as to
> what's the rationale behind this?

It looks like the minimum of a quadratic given f(x0), f'(x0) and f(x0+u).

-- 
Brian Gough