On Dec 14, 2007 12:28 PM, Daniel Lakeland <dlakelan at street-artists.org> wrote:
> For some decision theory type stuff I tried to use maxima to fit a
> polynomial to the piecewise linear tax code.
It should work OK to phrase an interpolation problem as a general
minimization problem, but doesn't Maxima have a function
to construct an interpolating polynomial or (probably better)
a polynomial spline?
> 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.
Well, that's not differentiable everywhere.
I think any method based on a gradient or Hessian will have trouble.
Istr least absolute deviation problems are solved via linear or quadratic
programming or something.
> lbfgs complains that it can't find a solution and the norm of the
> gradient is massive.
I've found that rescaling the variables often helps LBFGS.
But since the FOM isn't differentiable everywhere, that might
not make any difference.
> It's come up several times before that numerical optimizations are not
> terribly successful in maxima.
Has it? Maybe I have different expectations or something ...
Maybe we could throw in a gradient-free minimization method.
FWIW
Robert Dodier