nloptr (version 1.0.0)

sbplx: 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.

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.

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).

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 (?)