R: An R interface to the uobyqa implementation of Powell
uobyqa
R Documentation
An R interface to the uobyqa implementation of Powell
Description
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.
See Also
optim, nlminb
Examples
fr <- function(x) { ## Rosenbrock Banana function
100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}
(x3 <- uobyqa(c(1, 2), fr))
## => 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)
# To add if we can find them -- examples of ierr = 3.
providing 
.