On 4/16/07, Robert Dodier <robert.dodier at gmail.com> wrote:
> Looking at the plot made by plot3d for the function above, it is very
> bumpy. So it could well be that it is going to be difficult for any
> numerical method.
I have some code for minimization without derivatives. As Robert
observed the function is too bumpy to compute a minimum in 2d but you
I can get a minimum in 1d:
(%i9) brent(E(t, 0.1, 2^15), t, -2, 0);
(%o9) [t=-1.392488]
(%i10) E(t,0.1,2^15), %[1];
(%o10) -0.0011139
(%i11) brent(E(t, 0.1, 2^15), t, -4, -3.5);
(%o11) [t=-3.909836]
(%i12) E(t,0.1,2^15), %[1];
(%o12) -0.0011287
By lookin at the graph of E(t, 0.1, 2^15) it looks like this could be
a good approximation for the minimum.
brent is defined in powell.lisp (
http://wxmaxima.sourceforge.net/powell.lisp ) and there is also powell
which computes the minimum in more dimensions (but it does not work
for this function).
--
Andrej