newuoa: New Unconstrained Optimization with quadratic Approximation

In nloptr: R Interface to NLopt

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(), ...)

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.

Details

This is an algorithm derived from the NEWUOA 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

NEWUOA may be largely superseded by BOBYQA.

Author(s)

Hans W. Borchers

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).

See Also

bobyqa, cobyla

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

nloptr documentation built on July 4, 2024, 1:08 a.m.