From Prof. J C Nash

[zhenglei-gao]

I'm rather glad minpack.lm is available as I think the comparisons between it and nlmrt let us improve our codes. nlmrt is all in R, and I am acutely aware that it has some deficiencies. In particular, data must be passed in a data frame. So do not be shy about asking questions. I find interaction with problems and their authors help to bring the code forward.

The example in your StackOverflow posting (sent to me by Ben Bolker BTW) looks very much like something has stopped too soon when converging from a particular direction, and this is what I've been seeing sometimes with bounds constraints in nls.lm. Unfortunately, because the code is rather convoluted (I think in Fortran, but possibly now in C) it is difficult to add the bounds constraints to a code that was initially unconstrained.

[zhenglei-gao]

• Classic Powell
• Quasi Newton
• Simplex (Nelder-Mead)
• Genetic Algorithm
• Particle Swarm
• Trust Region Framework

[zhenglei-gao]

Trust Regrion Framwork:

1. Choose initial point $x_0$.
2. Create a local linear model around that point, and define an initial trust region radius, an area in which we think the model is good. Repeat:
   • Go to the minimizer(predicted optimum) of the model inside the trust region.
   • Verify: Does the error decrease?
   • If true and the if the model is very good, go further until quality gets worse, take last point as new center, reduce radius and calculate new model.
   • If just true, keep radius and calculate new model.
   • If not true, reduce size of the trust region.