nlminb {stats}R Documentation

Optimization using PORT routines

Description

Unconstrained and constrained optimization using PORT routines.

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 (possibly NA/Inf). 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.
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.
... Ffurther arguments to be supplied to objective.

Details

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

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

Control parameters

Possible names in the control list and their default values are:

eval.max
Maximum number of evaluations of the objective function allowed. Defaults to 200.
iter.max
Maximum number of iterations allowed. Defaults to 150.
trace
The value of the objective function and the parameters is printed every trace'th iteration. Defaults to 0 which indicates no trace information is to be printed.
abs.tol
Absolute tolerance. Defaults to 1e-20.
rel.tol
Relative tolerance. Defaults to 1e-10.
x.tol
X tolerance. Defaults to 1.5e-8.
step.min
Minimum step size. Defaults to 2.2e-14.

Author(s)

(of R port) Douglas Bates and Deepayan Sarkar.

References

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

See Also

optim 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, obj = 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, obj = sumsq, lower = -1, upper = 1, y = y)
# try using the gradient
sumsq.g <- function(x,y) 2*(x-y)
nlminb(start = x0, obj = sumsq, grad = 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, obj = sumsq, grad = sumsq.g, hes = 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))
[Package stats version 2.4.1 Index]