# 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 - 10*atan2(x, x)/(2*pi))^2 +
(sqrt(x^2 + x^2) - 1)^2 +x^2
x0 <- c(-1, 0, 0)
sbplx(x0, fphv)    #  1 0 0

# Powell's Singular Function (PSF)
psf <- function(x)  (x + 10*x)^2 + 5*(x - x)^2 +
(x - 2*x)^4 + 10*(x - x)^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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