An R interface to the uobyqa implementation of Powell

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

Usage

uobyqa(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:

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.
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.

Powell's Fortran code has been slightly modified (thanks to Doug Bates for help on this) to avoid use of PRINT statements. Output is now via calls to C routines set up to work with the routines BOBYQA, NEWUOA and UOBYQA.

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

The number of function evaluations used.

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
3: a trust region step failed to reduce q (Consult Powell for explanation.)

msg

A message describing the outcome of UOBYQA

References

M. J. D. Powell, "The uobyqa 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 uobyqa for minimization without derivatives", IMA Journal of Numerical Analysis, 2008; 28: 649-664.

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
}
(x3 <- uobyqa(c(1, 2), fr))
#> parameter estimates: 0.999999999966711, 0.999999999942818 
#> objective: 9.93797513608589e-21 
#> number of function evaluations: 61 
## => optimum at c(1, 1) with fval = 0
# check the error exits
# too many iterations
x3e<-uobyqa(c(1, 2), fr, control = list(maxfun=50))
str(x3e)
#> List of 5
#>  $ par  : num [1:2] 1 1
#>  $ fval : num 1.79e-08
#>  $ feval: int 50
#>  $ ierr : num 1
#>  $ msg  : chr "uobyqa -- maximum number of function evaluations exceeded"
#>  - attr(*, "class")= chr [1:2] "uobyqa" "minqa"


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