[R] nonlinear least squares fitting Trust-Region"

[Martin Ivanov]

Dear Mr Graves,
Thank you very much for your response. Nobody else from this mailing list ventured to reply to me for the two weeks since I posted my question.
"nlminb" and "optim" are just optimization procedures. What I need is not just optimization, but a nonlinear CURVE FITTING procedure. If there is some way to perform nonlinear curve fitting with the "Trust-Region" algorithm using any of these functions, I would me much obliged to you if you suggest to me how to achieve that. You asked me why I do not want Gauss-Newton. Since I am not an expert in the field of optimization, I am just conforming to what matlab documentation suggests, namely:
"Algorithm used for the fitting procedure: Trust-Region -- This is the default algorithm and must be used if you specify coefficient constraints. Levenberg-Marquardt -- If the trust-region algorithm does not produce a reasonable fit, and you do not have coefficient constraints, you should try the Levenberg-Marquardt algorithm. Gauss-Newton --THIS ALGORITHM IS POTENTIALLY FASTER THAN THE OTHER ALGORITHMS, BUT IT ASSUMES THAT THE RESIDUALS ARE CLOSE TO ZERO. IT IS INCLUDED FOR PEDAGOGICAL REASONS AND SHOULD BE THE LAST CHOICE FOR MOST MODELS AND DATA SETS. 
I browsed some literature about the garchfit function, but I did not see the "Trust-Region" algorithm there either: algorithm = c("sqp", "nlminb", "lbfgsb", "nlminb+nm", "lbfgsb+nm"), control = list(), title = NULL, description = NULL, ...)

Thank you for your attention. I am looking forward to your reply.
Regards,
Martin

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