# bobyqa: An R interface to the bobyqa implementation of Powell In minqa: Derivative-free optimization algorithms by quadratic approximation

## 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

 `1` ```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 `par` using auxiliary data in .... The first argument of `fn` must be `par`. `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 `fn`.

## 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] 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 `min(0.95, 0.2 * max(abs(par)))`. Note also that smallest difference `abs(upper-lower)` should be greater than or equal to `rhobeg*2`. If this is not the case then `rhobeg` 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 `0, 1, 2 or 3`, which controls the amount of printing. Specifically, there is no output if `iprint=0` and there is output only at 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`. 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` The number of function evaluations used. `ierr` An integer error code. A value of zero indicates success. Other values are 1maximum number of function evaluations exceeded 2NPT, the number of approximation points, is not in the required interval 3a trust region step failed to reduce q (Consult Powell for explanation.) 4one of the box constraint ranges is too small (< 2*RHOBEG) 5bobyqa 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 (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.

`optim`, `nlminb`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```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. ```

minqa documentation built on May 2, 2019, 4:53 p.m.