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.

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.

Details

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

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).

Examples


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)))
#> $par
#> [1] 0.5000000 0.2500000 0.4957871
#> 
#> $value
#> [1] 0.25
#> 
#> $iter
#> [1] 74
#> 
#> $convergence
#> [1] 4
#> 
#> $message
#> [1] "NLOPT_XTOL_REACHED: Optimization stopped because xtol_rel or xtol_abs (above) was reached."
#>