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, returning a single numeric
value. This should be a function with first argument a vector of
the length of If the function value has an attribute called 
p 
starting parameter values for the minimization. 
... 
additional arguments to be passed to 
hessian 
if 
typsize 
an estimate of the size of each parameter at the minimum. 
fscale 
an estimate of the size of 
print.level 
this argument determines the level of printing
which is done during the minimization process. The default
value of 
ndigit 
the number of significant digits in the function 
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 
stepmax 
a positive scalar which gives the maximum allowable
scaled step length. 
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. 
Note that arguments after ...
must be matched exactly.
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.
The functions supplied should always return finite (including not
NA
and not NaN
) values: for the function value itself
nonfinite values are replaced by the maximum positive value with a warning.
The parameter vector passed to f
and hessian
has special
semantics and is shared between calls. The functions should not copy it.
A list containing the following components:
minimum 
the value of the estimated minimum of 
estimate 
the point at which the minimum value of

gradient 
the gradient at the estimated minimum of 
hessian 
the hessian at the estimated minimum of 
code 
an integer indicating why the optimization process terminated.

iterations 
the number of iterations performed. 
The current code is by Saikat DebRoy and the R Core team, using a C translation of Fortran code by Richard H. Jones.
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) utils::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)