Description Usage Arguments Details Value References See Also Examples
The purpose of uobyqa
is to minimize a function of many variables
by a trust region method that forms quadratic models by interpolation.
1 
par 
A numeric vector of starting estimates. 
fn 
A function that returns the value of the objective at the
supplied set of 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 
Functions fn
must return a numeric value.
The control
argument is a list. Possible named values in the
list and their defaults are:
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.
The smallest value of the trust region radius that is allowed. If
not defined, then 1e6 times the value set for rhobeg
will be
used.
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
.
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.
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

msg 
A message describing the outcome of UOBYQA 
M. J. D. Powell, "The uobyqa software for unconstrained optimization without derivatives", in LargeScale 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: 649664.
Description was taken from comments in the Fortran code of M. J. D. Powell on which minqa is based.
1 2 3 4 5 6 7 8 9 10 11 12  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.

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