R: Optimization using PORT routines

nlminb {stats} | R Documentation

## 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.

### Details

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

If any of the functions returns `NA` or `NaN` this is an error for the gradient and Hessian, and such values for function evaluation are replaced by `+Inf` with a warning.

### 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 0 so the absolute convergence test is not used. If the objective function is known to be non-negative, the previous default of `1e-20` would be more appropriate.

`rel.tol`

  Relative tolerance. Defaults to `1e-10`.

`x.tol`

  X tolerance. Defaults to `1.5e-8`.

`xf.tol`

  false convergence tolerance. Defaults to `2.2e-14`.

`step.min, step.max`

  Minimum and maximum step size. Both default to `1.`.

sing.tol

  singular convergence tolerance; defaults to `rel.tol`.

scale.init

  ...

diff.g

  an estimated bound on the relative error in the objective function value.

### Author(s)

R port: Douglas Bates and Deepayan Sarkar.

Underlying Fortran code by David M. Gay

### Source

https://www.netlib.org/port/

### References

David M. Gay (1990), Usage summary for selected optimization routines. Computing Science Technical Report 153, AT&T Bell Laboratories, Murray Hill.

### 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))

[Package stats version 4.0.5 Index]