[R] How does nlm work?

[Frederico Zanqueta Poleto]

Dear R users,

I have looked in the reference
     Schnabel, R. B., Koontz, J. E. and Weiss, B. E. (1985) A modular
     system of algorithms for unconstrained minimization. _ACM Trans.
     Math. Software_, *11*, 419-440.
cited in the nlm help.

This article says that the algorithm permits the use of  step selection 
(line search, dogleg and optimal step), analytic or finite diference 
gradient and analytic, finite diference or BFGS Hessian aproximation.

Looking back in the nlm help, it has the information that:
a) it does just the line search step selecion;
b) it has the option to inform the gradient and the Hessian by 
attributes if the user wants.

My questions are:
1) When I do not supply the Hessian, the function does finite difference 
or BFGS approximation? (Is it possible to select one or other?)

2) I have already used the option to inform the gradient but I don't 
know how to inform the Hessian. Anybody has an example?

3) I have never heard of this step selections (line search, dogleg and 
optimal step). I would like to know something about it. I would 
appreciate if someone could send references for me to learn the subject.

Sincerely,

-- 
Frederico Zanqueta Poleto
fred at poleto.com
--
"An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem." J. W. Tukey