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(), ...)
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 |
... |
additional arguments passed to the function. |
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).
List with components:
par |
the optimal solution found so far. |
value |
the function value corresponding to |
iter |
number of (outer) iterations, see |
convergence |
integer code indicating successful completion (> 0) or a possible error number (< 0). |
message |
character string produced by NLopt and giving additional information. |
It is the request of Tom Rowan that reimplementations of his algorithm shall not use the name ‘subplex’.
T. Rowan, “Functional Stability Analysis of Numerical Algorithms”, Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, 1990.
subplex::subplex
# 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 (?)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.