# uobyqa: An R interface to the uobyqa implementation of Powell In minqa: Derivative-Free Optimization Algorithms by Quadratic Approximation

 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 1maximum number of function evaluations exceeded 3a 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.

`optim`, `nlminb`

### Examples

```fr <- function(x) {   ## Rosenbrock Banana function
100 * (x - x^2)^2 + (1 - x)^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.

```

minqa documentation built on Oct. 19, 2022, 9:05 a.m.