newuoa: New Unconstrained Optimization with quadratic Approximation
Description
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.
Usage
newuoa(x0, fn, nl.info = FALSE, control = list(), ...)
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.
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.
Author
Hans W. Borchers
Details
This is an algorithm derived from the NEWUOA Fortran subroutine of
Powell, converted to C and modified for the NLopt stopping
criteria.
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).
## Rosenbrock Banana functionrbf <- 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