sbplx

0th

Percentile

Subplex Algorithm

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.

subplex::subplex

• sbplx
Examples
# NOT RUN {
# 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 (?)

# }
`
Documentation reproduced from package nloptr, version 1.2.1, License: LGPL-3

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