For some decision theory type stuff I tried to use maxima to fit a
polynomial to the piecewise linear tax code. It's easier to use a
smooth approximate tax function when doing optimizations later, so I
hoped that maxima would do this relatively simple fit.
Using the interpol code I was able to construct the piecewise linear
taxation function, and then construct a tax table for $1000 increments
from 0 to 300000. I created a figure of merit function that takes the
maximum absolute deviation from the tax table. Unfortunately I
couldn't get LBFGS to converge. By plotting the 3d surface I was able
to find a decent starting point, but lbfgs complains that it can't
find a solution and the norm of the gradient is massive. It may in
fact be a sharp minimum due to the non-smooth nature of the function,
and in any case it seems unlikely that the symbolic gradient of the
figure of merit is very helpful.
It's come up several times before that numerical optimizations are not
terribly successful in maxima. Has anyone got a purely numerical
optimizer that they use in maxima that might be added to the
contributed code?
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan