[R] Nonlinear regression / Curve fitting with L-infinity norm

Jack Fruit downitoo at yahoo.com
Fri Mar 30 11:31:40 CEST 2012

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:

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.

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