stats (version 3.3)

nlminb: Optimization using PORT routines

Description

Unconstrained and box-constrained optimization using PORT routines.

For historical compatibility.

Usage

nlminb(start, objective, gradient = NULL, hessian = NULL, ...,
       scale = 1, control = list(), lower = -Inf, upper = Inf)

Arguments

start

numeric vector, initial values for the parameters to be optimized.

objective

Function to be minimized. Must return a scalar value. The first argument to objective is the vector of parameters to be optimized, whose initial values are supplied through start. Further arguments (fixed during the course of the optimization) to objective may be specified as well (see ...).

gradient

Optional function that takes the same arguments as objective and evaluates the gradient of objective at its first argument. Must return a vector as long as start.

hessian

Optional function that takes the same arguments as objective and evaluates the hessian of objective at its first argument. Must return a square matrix of order length(start). Only the lower triangle is used.

...

Further arguments to be supplied to objective.

scale

See PORT documentation (or leave alone).

control

A list of control parameters. See below for details.

lower, upper

vectors of lower and upper bounds, replicated to be as long as start. If unspecified, all parameters are assumed to be unconstrained.

Value

• A list with components:
• par
  The best set of parameters found.
• objective
  The value of objective corresponding to par.
• convergence
  An integer code. 0 indicates successful convergence.
• message
  A character string giving any additional information returned by the optimizer, or NULL. For details, see PORT documentation.
• iterations
  Number of iterations performed.
• evaluations
  Number of objective function and gradient function evaluations

source

http://netlib.bell-labs.com/netlib/port/

Details

Any names of start are passed on to objective and where applicable, gradient and hessian. The parameter vector will be coerced to double.

The PORT documentation is at http://netlib.bell-labs.com/cm/cs/cstr/153.pdf.

The parameter vector passed to objective, gradient and hessian had special semantics prior to R3.1.0 and was shared between calls. The functions should not copy it.

If any of the functions returns NA or NaN the internal code could infinite-loop in Rprior to 2.15.2: this is now an error for the gradient and Hessian, and such values for function evaluation are replaced by +Inf with a warning.

See Also

optim (which is preferred) and nlm.

optimize for one-dimensional minimization and constrOptim for constrained optimization.

Examples

x <- rnbinom(100, mu = 10, size = 10)
hdev <- function(par)
    -sum(dnbinom(x, mu = par[1], size = par[2], log = TRUE))
nlminb(c(9, 12), hdev)
nlminb(c(20, 20), hdev, lower = 0, upper = Inf)
nlminb(c(20, 20), hdev, lower = 0.001, upper = Inf)

## slightly modified from the S-PLUS help page for nlminb
# this example minimizes a sum of squares with known solution y
sumsq <- function( x, y) {sum((x-y)^2)}
y <- rep(1,5)
x0 <- rnorm(length(y))
nlminb(start = x0, sumsq, y = y)
# now use bounds with a y that has some components outside the bounds
y <- c( 0, 2, 0, -2, 0)
nlminb(start = x0, sumsq, lower = -1, upper = 1, y = y)
# try using the gradient
sumsq.g <- function(x, y) 2*(x-y)
nlminb(start = x0, sumsq, sumsq.g,
       lower = -1, upper = 1, y = y)
# now use the hessian, too
sumsq.h <- function(x, y) diag(2, nrow = length(x))
nlminb(start = x0, sumsq, sumsq.g, sumsq.h,
       lower = -1, upper = 1, y = y)

## Rest lifted from optim help page

fr <- function(x) {   ## Rosenbrock Banana function
    x1 <- x[1]
    x2 <- x[2]
    100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
grr <- function(x) { ## Gradient of 'fr'
    x1 <- x[1]
    x2 <- x[2]
    c(-400 * x1 * (x2 - x1 * x1) - 2 * (1 - x1),
       200 *      (x2 - x1 * x1))
}
nlminb(c(-1.2,1), fr)
nlminb(c(-1.2,1), fr, grr)


flb <- function(x)
    { p <- length(x); sum(c(1, rep(4, p-1)) * (x - c(1, x[-p])^2)^2) }
## 25-dimensional box constrained
## par[24] is *not* at boundary
nlminb(rep(3, 25), flb, lower = rep(2, 25), upper = rep(4, 25))
## trying to use a too small tolerance:
r <- nlminb(rep(3, 25), flb, control = list(rel.tol = 1e-16))
stopifnot(grepl("rel.tol", r$message))