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Constraint violation by FindMinimum w/ 2nd-start arg(?)


Hi everyone,

I'm using the latest Mathematica 5.0.1 on Win2k (this is the one with advanced
docs for Optimization, particularly FindMinimum).

I'm trying to do:
  FindMinimum[f[x], {x, x0,x1,xmin,xmax}]

The advanced docs state that the addition of the "2nd-start" argument
x1 will automatically force FindMinimum to employ numeric
("finite-difference") evaluation rather than symbolic evaluation of
the gradient (and hessian...), and indeed it does, given the vast
speedup on my f[x].

However, by omitting x1, FindMinimum respects the constraints xmin,
xmax (i.e., the solution must lie within those bounds).  Including x1
causes constraint violation.

Is this a "feature" or a bug?  I suppose it might make sense that an
analytic gradient could better respect the constraints, but I'm pretty
sure that Mathematica is falling-back into numerical evaluation of the
gradient of my f[x] when I omit the x1 argument anyhow (f[x] involves
pseudoinverse of g[x], where g[] are interpolatingfunction's).

Regards,


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