# bobyqa

0th

Percentile

##### Bound Optimization by Quadratic Approximation

BOBYQA performs derivative-free bound-constrained optimization using an iteratively constructed quadratic approximation for the objective function.

##### Usage
bobyqa(x0, fn, lower = NULL, upper = NULL, nl.info = FALSE,
control = list(), ...)
##### Arguments
x0

starting point for searching the optimum.

fn

objective function that is to be minimized.

lower, upper

lower and upper bound constraints.

nl.info

logical; shall the original NLopt info been shown.

control

list of options, see nl.opts for help.

...

additional arguments passed to the function.

##### Details

This is an algorithm derived from the BOBYQA Fortran subroutine of Powell, converted to C and modified for the NLOPT stopping criteria.

##### Value

List with components:

par

the optimal solution found so far.

value

the function value corresponding to par.

iter

number of (outer) iterations, see maxeval.

convergence

integer code indicating successful completion (> 0) or a possible error number (< 0).

message

character string produced by NLopt and giving additional information.

##### Note

Because BOBYQA constructs a quadratic approximation of the objective, it may perform poorly for objective functions that are not twice-differentiable.

##### References

M. J. D. Powell. The BOBYQA algorithm for bound constrained optimization without derivatives,'' Department of Applied Mathematics and Theoretical Physics, Cambridge England, technical reportNA2009/06 (2009).

cobyla, newuoa

• bobyqa
##### Examples
# NOT RUN {
fr <- function(x) {   ## Rosenbrock Banana function
100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}
(S <- bobyqa(c(0, 0, 0), fr, lower = c(0, 0, 0), upper = c(0.5, 0.5, 0.5)))

# }

Documentation reproduced from package nloptr, version 1.2.1, License: LGPL-3

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