Optimization using PORT routines

Unconstrained and box-constrained optimization using PORT routines.

For historical compatibility.

nlminb(start, objective, gradient = NULL, hessian = NULL, ...,
       scale = 1, control = list(), lower = -Inf, upper = Inf)
numeric vector, initial values for the parameters to be optimized.
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 ...).
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.
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.
See PORT documentation (or leave alone).
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.

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

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.


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


See Also

optim (which is preferred) and nlm.

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

  • nlminb
library(stats) 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))
Documentation reproduced from package stats, version 3.3, License: Part of R 3.3

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