R: Examples for 'stats::nlminb'

### ** Examples
## No test: 
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)

$par
[1]  9.950003 13.495939

$objective
[1] 280.5877

$convergence
[1] 0

$iterations
[1] 10

$evaluations
function gradient 
      12       30 

$message
[1] "relative convergence (4)"

nlminb(c(20, 20), hdev, lower = 0, upper = Inf)

$par
[1]  9.95000 13.49592

$objective
[1] 280.5877

$convergence
[1] 0

$iterations
[1] 16

$evaluations
function gradient 
      20       40 

$message
[1] "relative convergence (4)"

nlminb(c(20, 20), hdev, lower = 0.001, upper = Inf)

$par
[1]  9.95000 13.49592

$objective
[1] 280.5877

$convergence
[1] 0

$iterations
[1] 16

$evaluations
function gradient 
      20       40 

$message
[1] "relative convergence (4)"

## 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)

$par
[1] 1 1 1 1 1

$objective
[1] 1.056396e-18

$convergence
[1] 0

$iterations
[1] 5

$evaluations
function gradient 
       7       33 

$message
[1] "X-convergence (3)"

# 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)

$par
[1] -4.307913e-08  1.000000e+00  1.436043e-06 -1.000000e+00  9.380389e-07

$objective
[1] 2

$convergence
[1] 0

$iterations
[1] 4

$evaluations
function gradient 
       6       20 

$message
[1] "relative convergence (4)"

# try using the gradient
sumsq.g <- function(x, y) 2*(x-y)
nlminb(start = x0, sumsq, sumsq.g,
       lower = -1, upper = 1, y = y)

$par
[1] -1.110223e-16  1.000000e+00 -2.428613e-17 -1.000000e+00 -1.387779e-16

$objective
[1] 2

$convergence
[1] 0

$iterations
[1] 4

$evaluations
function gradient 
       6        4 

$message
[1] "both X-convergence and relative convergence (5)"

# 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)

$par
[1]  2.220446e-16  1.000000e+00  0.000000e+00 -1.000000e+00  5.551115e-17

$objective
[1] 2

$convergence
[1] 0

$iterations
[1] 2

$evaluations
function gradient 
       4        2 

$message
[1] "both X-convergence and relative convergence (5)"

## 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)

$par
[1] 1 1

$objective
[1] 2.768493e-20

$convergence
[1] 0

$iterations
[1] 35

$evaluations
function gradient 
      44       74 

$message
[1] "X-convergence (3)"

nlminb(c(-1.2,1), fr, grr)

$par
[1] 1 1

$objective
[1] 4.291816e-22

$convergence
[1] 0

$iterations
[1] 35

$evaluations
function gradient 
      43       36 

$message
[1] "X-convergence (3)"

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))

$par
 [1] 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000
 [9] 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000
[17] 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.109093
[25] 4.000000

$objective
[1] 368.1059

$convergence
[1] 0

$iterations
[1] 6

$evaluations
function gradient 
      10      177 

$message
[1] "relative convergence (4)"

## 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))
## End(No test)

Examples for 'stats::nlminb'

Optimization using PORT routines