An R interface to the NEWUOA implementation of Powell

The purpose of newuoa is to minimize a function of many variables by a trust region method that forms quadratic models by interpolation.

Usage

newuoa(par, fn, control = list(), ...)

Arguments

par: A numeric vector of starting estimates.
fn: A function that returns the value of the objective at the supplied set of parameters par using auxiliary data in .... The first argument of fn must be par.
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 fn.

Details

Functions fn must return a numeric value. The control argument is a list; possible named values in the list and their defaults are:

npt: 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: 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)
rhoend: The smallest value of the trust region radius that is allowed. If not defined, then 1e-6 times the value set for rhobeg will be used.
iprint: 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.
maxfun: The maximum allowed number of function evaluations. If this is exceeded, the method will terminate.

Value

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

1: maximum number of function evaluations exceeded
2: NPT, the number of approximation points, is not in the required interval
3: a trust region step failed to reduce q (Consult Powell for explanation.)
5: newuoa detected too much cancellation in denominator (We have not fully understood Powell's code to explain this.)

msg

A message describing the outcome of UOBYQA

References

M. J. D. Powell, "The NEWUOA software for unconstrained optimization without derivatives", in Large-Scale 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: 649-664.

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.

Examples

fr <- function(x) {   ## Rosenbrock Banana function
    100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}
(x2 <- newuoa(c(1, 2), fr))
#> parameter estimates: 1.00000116212176, 1.00000231682727 
#> objective: 1.35602908489591e-12 
#> number of function evaluations: 136 
## => 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)
#> List of 5
#>  $ par  : num [1:2] 1.37 1.89
#>  $ fval : num 0.139
#>  $ feval: int 50
#>  $ ierr : num 1
#>  $ msg  : chr "newuoa -- maximum number of function evaluations exceeded"
#>  - attr(*, "class")= chr [1:2] "newuoa" "minqa"

# Throw an error because npt is too small -- does NOT work as of 2010-8-10 as 
#    minqa.R seems to force a reset.
x2n<-newuoa(c(2,2), fr, control=list(npt=1))
str(x2n)
#> List of 5
#>  $ par  : num [1:2] 1 1
#>  $ fval : num 1.43e-15
#>  $ feval: int 193
#>  $ ierr : int 0
#>  $ msg  : chr "Normal exit from newuoa"
#>  - attr(*, "class")= chr [1:2] "newuoa" "minqa"

# To add if we can find them -- examples of ierr = 3 and ierr = 5.