sbplx() R function from [nloptr]

Subplex Algorithm

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


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.

Returns

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

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.

Note

It is the request of Tom Rowan that reimplementations of his algorithm shall not use the name `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 (?)

References

T. Rowan, ``Functional Stability Analysis of Numerical Algorithms'', Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, 1990.

sbplx function