newuoa  R Documentation 
The purpose of newuoa
is to minimize a function of many variables
by a trust region method that forms quadratic models by interpolation.
newuoa(par, fn, control = list(), ...)
par 
A numeric vector of starting estimates. 
fn 
A function that returns the value of the objective at the
supplied set of parameters 
control 
An optional list of control settings. See the details section for the names of the settable control values and their effect. 
... 
Further arguments to be passed to 
Functions fn
must return a numeric value.
The control
argument is a list; possible named values in the
list and their defaults are:
The number of points used to approximate the objective function
via a quadratic approximation. The value of npt must be in the
interval [n+2,(n+1)(n+2)/2] where n is the number of
parameters in par
. Choices that exceed 2*n+1 are not
recommended. If not defined, it will be set to min(n * 2, n+2).
rhobeg
and rhoend
must be set to the initial and final
values of a trust region radius, so both must be positive with
0 < rhoend < rhobeg
. Typically rhobeg
should be about
one tenth of the greatest expected change to a variable. If the
user does not provide a value, this will be set to max(par)
/ 2)
The smallest value of the trust region radius that is allowed. If
not defined, then 1e6 times the value set for rhobeg
will be
used.
The value of iprint
should be set to an integer value in
0, 1, 2, 3, ...
,
which controls the amount of printing. Specifically, there is no
output if iprint=0
and there is output only at the start
and the return if
iprint=1
. Otherwise, each new value of rho
is printed,
with the best vector of variables so far and the corresponding value
of the objective function. Further, each new value of the objective
function with its variables are output if iprint=3
.
If iprint > 3
, the objective
function value and corresponding variables are output every iprint
evaluations.
Default value is 0
.
The maximum allowed number of function evaluations. If this is exceeded, the method will terminate.
A list with components:
par 
The best set of parameters found. 
fval 
The value of the objective at the best set of parameters found. 
feval 
Number of function evaluations to determine the optimum 
ierr 
An integer error code. A value of zero indicates success. Other values (consistent with BOBYQA values) are

msg 
A message describing the outcome of UOBYQA 
M. J. D. Powell, "The NEWUOA software for unconstrained optimization without derivatives", in LargeScale Nonlinear Optimization, Series: Nonconvex Optimization and Its Applications , Vol. 83, Di Pillo, Gianni; Roma, Massimo (Eds.) 2006, New York: Springer US.
M. J. D. Powell, "Developments of NEWUOA for minimization without derivatives" IMA Journal of Numerical Analysis, 2008; 28: 649664.
M. J. D. Powell (2007) "Developments of NEWUOA for unconstrained minimization without derivatives" Cambridge University, Department of Applied Mathematics and Theoretical Physics, Numerical Analysis Group, Report NA2007/05, http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2007_05.pdf.
Description was taken from comments in the Fortran code of M. J. D. Powell on which minqa is based.
optim
, nlminb
fr < function(x) { ## Rosenbrock Banana function 100 * (x[2]  x[1]^2)^2 + (1  x[1])^2 } (x2 < newuoa(c(1, 2), fr)) ## => optimum at c(1, 1) with fval = 0 # check the error exits # too many iterations x2e<newuoa(c(1, 2), fr, control = list(maxfun=50)) str(x2e) # Throw an error because npt is too small  does NOT work as of 2010810 as # minqa.R seems to force a reset. x2n<newuoa(c(2,2), fr, control=list(npt=1)) str(x2n) # To add if we can find them  examples of ierr = 3 and ierr = 5.
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