sbplx: Subplex Algorithm

In nloptr: R Interface to NLopt

Subplex Algorithm

Description

Subplex is a variant of Nelder-Mead that uses Nelder-Mead on a sequence of subspaces.

Usage

sbplx(
  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.

Details

SUBPLEX is claimed to be much more efficient and robust than the original Nelder-Mead while retaining the latter's facility with discontinuous objectives.

This implementation has explicit support for bound constraints via the method in the Box paper as described on the neldermead help page.

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

It is the request of Tom Rowan that reimplementations of his algorithm shall not use the name ‘subplex’.

References

T. Rowan, “Functional Stability Analysis of Numerical Algorithms”, Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, 1990.

See Also

subplex::subplex

Examples

# Fletcher and Powell's helic valley
fphv <- function(x)
  100*(x[3] - 10*atan2(x[2], x[1])/(2*pi))^2 +
    (sqrt(x[1]^2 + x[2]^2) - 1)^2 +x[3]^2
x0 <- c(-1, 0, 0)
sbplx(x0, fphv)  #  1 0 0

# Powell's Singular Function (PSF)
psf <- function(x)  (x[1] + 10*x[2])^2 + 5*(x[3] - x[4])^2 +
          (x[2] - 2*x[3])^4 + 10*(x[1] - x[4])^4
x0 <- c(3, -1, 0, 1)
sbplx(x0, psf, control = list(maxeval = Inf, ftol_rel = 1e-6)) #  0 0 0 0 (?)

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