I thought maybe my suggestion for reparameterizing this simple problem was ignored because I didn't supply R code for the problem. Here it is using optim for the optimization. It converges trivially with an initial value for E of 1000. As I stated before, there is nothing at all difficult about this problem. You simply need to parameterize it properly. Of course that is not to say that rescaling is not useful as well, but the important thing is to parameterize the model properly.
ExponValues=c(2018.34,2012.54,2018.85,2023.52,2054.58,2132.61,2247.17,2468.32,27 78.47) Expon=c(17,18,19,20,21,22,23,24,25) # Example starting estimate calculation E=1000.0 y1=2018 yn=2778.47 nobs=9 #keep y1 and yn fixed and get initial value for E Esp1 <- optim(c(E=E),method ="BFGS", function(x) { E=x[1] a=(yn-y1)/(E^Expon[nobs]-E^Expon[1]) Y0=y1-a*E^Expon[1]; diff=ExponValues-(Y0+a*E^ExponCycles) return(1000*sum(diff*diff)) })$par E=Esp1[1] Esp <- optim(c(y1=y1,yn=yn,E=E),method ="BFGS", function(x) { E=x[3] a=(x[2]-x[1])/(E^Expon[nobs]-E^Expon[1]) Y0=x[1]-a*E^Expon[1]; diff=ExponValues-(Y0+a*E^ExponCycles) return(1000*sum(diff*diff)) })$par y1=Esp[1] y2=Esp[2] E=Esp[3] a=(y2-y1)/(E^Expon[nobs]-E^Expon[1]) Y0=y1-a*E^Expon[1]; -- David A. Fournier P.O. Box 2040, Sidney, B.C. V8l 3S3 Canada Phone/FAX 250-655-3364 http://otter-rsch.com ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.