newuoa: New Unconstrained Optimization with quadratic Approximation

Description

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

Usage

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

Arguments

starting point for searching the optimum.

objective function that is to be minimized.

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:
parthe optimal solution found so far.
valuethe function value corresponding to par.
iternumber of (outer) iterations, see maxeval.
convergenceinteger code indicating successful completion (> 0) or a possible error number (< 0).
messagecharacter 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.

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

Run this code

fr <- function(x) {   ## Rosenbrock Banana function
    100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
}
(S <- newuoa(c(1, 2), fr))

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