[Help-gsl] Rationale behind intermediate_point()

[Johan Hattne]

Dear all;

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?

// Best wishes; Johan