New Unconstrained Optimization with quadratic Approximation

NEWUOA solves quadratic subproblems in a spherical trust region via a truncated conjugate-gradient algorithm. For bound-constrained problems, BOBYQA should be used instead, as Powell developed it as an enhancement thereof for bound constraints.

newuoa(x0, fn, nl.info = FALSE, control = list(), ...)

Arguments

x0: starting point for searching the optimum.
fn: objective function that is to be minimized.
nl.info: logical; shall the original NLopt info be 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 NEWUOA Fortran subroutine of Powell, converted to C and modified for the NLopt stopping criteria.

Note

NEWUOA may be largely superseded by BOBYQA.

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).

Author

Hans W. Borchers

Examples


## Rosenbrock Banana function

rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2}

S <- newuoa(c(1, 2), rbf)

## The function as written above has a minimum of 0 at (1, 1)

S
#> $par
#> [1] 1 1
#> 
#> $value
#> [1] 0
#> 
#> $iter
#> [1] 33
#> 
#> $convergence
#> [1] 1
#> 
#> $message
#> [1] "NLOPT_SUCCESS: Generic success return value."
#>