R help - Mar 2012 - Nonlinear regression / Curve fitting with L-infinity norm

Hello everyone,
I am looking into time series data compression at the moment. 
The idea is to fit a curve on a time series of n points so that the maximum
deviation on any of the points is not greater than a given
threshold. In other words, none of the values that the curve takes at the points
where the time series is defined, should be "further away" than a
certain threshold from the actual values.
Till now I have found out how to do nonlinear regression using the least squares
estimation method in R (nls function), but I haven't found any packages that
implement nonlinear regression with the L-infinity norm.
I have found literature on the subject, but haven't yet had the chance to
read it through:
http://www.jstor.org/discover/10.2307/2006101?uid=3737864&uid=2&uid=4&sid=21100693651721
or
http://www.dtic.mil/dtic/tr/fulltext/u2/a080454.pdf


I could try to implement this in R for instance, but I first looking to see if
this hasn't already been done and that I could maybe reuse it.


I have found a solution that I don't believe to be "very
scientific": I use nonlinear least squares regression to find the starting
values of the parameters which I subsequently use as starting points in the R
"optim" function that minimizes the maximum deviation of the curve
from the actual points.


Any help would be appreciated. The idea is to be able to find out if this type
of curve-fitting is possible on a given time series sequence and to determine
the parameters that allow it.


I hope there are other people that have already encountered this problem out
there and that could help me.
Thank you.