nlm number of function evaluations per iteration?

Question

I use nlm to maximize a likelihood in R. I would like to predict the number of likelihood evaluations and abort if the task is likely to take too long. nlm returns the number of 'iterations' (typically 10-20), and I take it that each iteration involves one numerical evaluation of the Hessian. Time for each iteration (Hessian?) depends on the number of parameters. So I'd like to know: What is the general relationship between the number of parameters and the number of function evaluations per iteration in nlm?

Answer 1

The question is very general, and so is my answer.

From the reference of nlm:

If the function value has an attribute called gradient or both gradient and hessian attributes, these will be used in the calculation of updated parameter values. Otherwise, numerical derivatives are used. deriv returns a function with suitable gradient attribute and optionally a hessian attribute.

If you provide the gradient and the Hessian for a function being minimized, each iteration involves two function evaluations. If you don't, the Hessian and the gradient are calculated numerically. The source code can be found here. As far as I understand, the parameters of the R nlm function only affect the number of iterations until convergence, but have no influence on the way gradients are evaluated numerically.