bobyqa {minqa} | R Documentation |
An R interface to the bobyqa implementation of Powell
Description
The purpose of bobyqa
is to minimize a function of many variables
by a trust region method that forms quadratic models by interpolation.
Box constraints (bounds) on the parameters are permitted.
Usage
bobyqa(par, fn, lower = -Inf, upper = Inf, control = list(), ...)
Arguments
par |
A numeric vector of starting estimates of the parameters of the objective function. |
fn |
A function that returns the value of the objective at the
supplied set of parameters |
lower |
A numeric vector of lower bounds on the parameters. If the length is 1 the single lower bound is applied to all parameters. |
upper |
A numeric vector of upper bounds on the parameters. If the length is 1 the single upper bound is applied to all 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 |
Details
The function fn
must return a scalar 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]
wheren
is the number of parameters inpar
. Choices that exceed2*n+1
are not recommended. If not defined, it will be set to\min(n * 2, n+2)
. - rhobeg
-
rhobeg
andrhoend
must be set to the initial and final values of a trust region radius, so both must be positive with0 < rhoend < rhobeg
. Typicallyrhobeg
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 tomin(0.95, 0.2 * max(abs(par)))
. Note also that smallest differenceabs(upper-lower)
should be greater than or equal torhobeg*2
. If this is not the case thenrhobeg
will be adjusted. - 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 in0, 1, 2, 3, ...
, which controls the amount of printing. Specifically, there is no output ifiprint=0
and there is output only at the start and the return ifiprint=1
. Otherwise, each new value ofrho
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 ifiprint=3
. Ifiprint > 3
, the objective function value and corresponding variables are output everyiprint
evaluations. Default value is0
. - 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 |
The number of function evaluations used. |
ierr |
An integer error code. A value of zero indicates success. Other values are
|
msg |
A message describing the outcome of UOBYQA |
References
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.
M. J. D. Powell (2009), "The BOBYQA algorithm for bound constrained optimization without derivatives", Report No. DAMTP 2009/NA06, Centre for Mathematical Sciences, University of Cambridge, UK. http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf.
Description was taken from comments in the Fortran code of M. J. D. Powell on which minqa is based.
See Also
Examples
fr <- function(x) { ## Rosenbrock Banana function
100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}
(x1 <- bobyqa(c(1, 2), fr, lower = c(0, 0), upper = c(4, 4)))
## => optimum at c(1, 1) with fval = 0
str(x1) # see that the error code and msg are returned
# check the error exits
# too many iterations
x1e<-bobyqa(c(1, 2), fr, lower = c(0, 0), upper = c(4, 4), control = list(maxfun=50))
str(x1e)
# Throw an error because bounds too tight
x1b<-bobyqa(c(4,4), fr, lower = c(0, 3.9999999), upper = c(4, 4))
str(x1b)
# Throw an error because npt is too small -- does NOT work as of 2010-8-10 as
# minqa.R seems to force a reset.
x1n<-bobyqa(c(2,2), fr, lower = c(0, 0), upper = c(4, 4), control=list(npt=1))
str(x1n)
# To add if we can find them -- examples of ierr = 3 and ierr = 5.