Return to Answer

I've included the Python 3 code used to generate the plots in case that's helpful. The script below receives and amplitude and a wavelength as positional arguments when run from the command-line.

I've included the Python 3 code used to generate the plots in case that's helpful. The script below receives an amplitude and a wavelength as positional arguments when run from the command-line.

For a concrete example on the real line, I had a play at finding the global minimum of $x\longmapsto x^2 + \sin(1000 x)$ with different initial conditions:

Zooming in to look at what went wrong for BFGS:

I've included the Python 3 code used to generate the plots in case that's helpful :)

For a concrete example on the real line, I had a play at finding the global minimum of $x\longmapsto x^2 + \sin(1000 x)$ with different initial conditions and marked the minima found by Nelder-Mead (blue dot) and BFGS (orange dot).

Zooming in to look at what went wrong for BFGS, it seems pretty likely that it's been thwarted by the 'microscopic' oscillations:

I've included the Python 3 code used to generate the plots in case that's helpful. The script below receives and amplitude and a wavelength as positional arguments when run from the command-line.

For a concrete example on the real line, I had a play at finding the global minimum of $x\longmapsto x^2 + \sin(1000 x)$ with different initial conditions.

Below is the Python 3 code used to generate the plots.

For a concrete example on the real line, I had a play at finding the global minimum of $x\longmapsto x^2 + \sin(1000 x)$ with different initial conditions:

I've included the Python 3 code used to generate the plots in case that's helpful :)