nlm {stats}  R Documentation 
This function carries out a minimization of the function f
using a Newtontype algorithm. See the references for details.
nlm(f, p, hessian = FALSE, typsize=rep(1, length(p)), fscale=1, print.level = 0, ndigit=12, gradtol = 1e6, stepmax = max(1000 * sqrt(sum((p/typsize)^2)), 1000), steptol = 1e6, iterlim = 100, check.analyticals = TRUE, ...)
f 
the function to be minimized. 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. This should be a function of a vector of
the length of p followed by any other arguments specified
by the ... argument. 
p 
starting parameter values for the minimization. 
hessian 
if TRUE , the hessian of f
at the minimum is returned. 
typsize 
an estimate of the size of each parameter at the minimum. 
fscale 
an estimate of the size of f at the minimum. 
print.level 
this argument determines the level of printing
which is done during the minimization process. The default
value of 0 means that no printing occurs, a value of 1
means that initial and final details are printed and a value
of 2 means that full tracing information is printed. 
ndigit 
the number of significant digits in the function f . 
gradtol 
a positive scalar giving the tolerance at which the
scaled gradient is considered close enough to zero to
terminate the algorithm. The scaled gradient is a
measure of the relative change in f in each direction
p[i] divided by the relative change in p[i] . 
stepmax 
a positive scalar which gives the maximum allowable
scaled step length. stepmax is used to prevent steps which
would cause the optimization function to overflow, to prevent the
algorithm from leaving the area of interest in parameter space, or to
detect divergence in the algorithm. stepmax would be chosen
small enough to prevent the first two of these occurrences, but should
be larger than any anticipated reasonable step. 
steptol 
A positive scalar providing the minimum allowable relative step length. 
iterlim 
a positive integer specifying the maximum number of iterations to be performed before the program is terminated. 
check.analyticals 
a logical scalar specifying whether the analytic gradients and Hessians, if they are supplied, should be checked against numerical derivatives at the initial parameter values. This can help detect incorrectly formulated gradients or Hessians. 
... 
additional arguments to f . 
If a gradient or hessian is supplied but evaluates to the wrong mode
or length, it will be ignored if check.analyticals = TRUE
(the
default) with a warning. The hessian is not even checked unless the
gradient is present and passes the sanity checks.
From the three methods available in the original source, we always use method “1” which is line search.
A list containing the following components:
minimum 
the value of the estimated minimum of f . 
estimate 
the point at which the minimum value of
f is obtained. 
gradient 
the gradient at the estimated minimum of f . 
hessian 
the hessian at the estimated minimum of f (if
requested). 
code 
an integer indicating why the optimization process terminated.

iterations 
the number of iterations performed. 
Dennis, J. E. and Schnabel, R. B. (1983) Numerical Methods for Unconstrained Optimization and Nonlinear Equations. PrenticeHall, Englewood Cliffs, NJ.
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.
constrOptim
for constrained optimization,
optimize
for onedimensional
minimization and uniroot
for root finding.
deriv
to calculate analytical derivatives.
For nonlinear regression, nls
may be better.
f < function(x) sum((x1:length(x))^2) nlm(f, c(10,10)) nlm(f, c(10,10), print.level = 2) str(nlm(f, c(5), hessian = TRUE)) f < function(x, a) sum((xa)^2) nlm(f, c(10,10), a=c(3,5)) f < function(x, a) { res < sum((xa)^2) attr(res, "gradient") < 2*(xa) res } nlm(f, c(10,10), a=c(3,5)) ## more examples, including the use of derivatives. ## Not run: demo(nlm)