Several books/papers have been discussed the problems of estimating the parameters and analysing the data of non-linear models. Some of which are:
1. Douglas M. Bates Donald G. WattsNonlinear Regression Analysis and Its Applications, 2008 https://doi.org/10.1002/9780470316757.refs
2. Kenneth Berk. Nonlinear Regression, 2012
3. Gordon K. Smyth. Nonlinear Regression, 2006 https://doi.org/10.1002/9780470057339.van017
4. Shyamal D. Peddada and Joseph K. Haseman. ANALYSIS OF NONLINEAR Regression Models: A cautionary note. Dose-Response, 3: 342–352, 2005 DOI: 10.2203/dose-response.003.03.005.
5. Lídia Raquel de Carvalho; Sheila Zambello de Pinho; Martha Maria Mischan. Methods to verify parameter equality in nonlinear regression models. Sci. Agric. (Piracicaba, Braz.), v.67, n.2, p.218-222, March/April 2010.
6. Ursula U. Müller. Estimating linear functionals in nonlinear regression with responses missing at random. Ann. Statist.Volume 37, Number 5A (2009), 2245-2277.
7. Godsland IF1, Agbaje OF, Hovorka R. Evaluation of nonlinear regression approaches to estimation of insulin sensitivity by the minimal model with reference to Bayesian hierarchical analysis. Am J Physiol Endocrinol Metab. 2006 Jul;291(1):E167-74. Epub 2006 Feb 14.
This looks straightforward. Regression is done in eviews by clicking QUICK and then ESTIMATE EQUATION.. Then the regression equation is written. Even if the regression is nonlinear the software will compute it.
Sometimes the type of regression may be specified amongst the options. For example Arch/garch, SLS, etc. are among the options.