multistart function

General-purpose optimization - multiple starts

Multiple initial parameter wrapper function that calls other R tools for optimization, including the existing optimr() function. UTF-8

multistart(parmat, fn, gr=NULL, lower=-Inf, upper=Inf, 
            method=NULL, hessian=FALSE,
            control=list(),
             ...)

Arguments

• parmat: a matrix of which each row is a set of initial values for the parameters for which optimal values are to be found. Names on the elements of this vector are preserved and used in the results data frame.

• fn: A function to be minimized (or maximized), with first argument the vector of parameters over which minimization is to take place. It should return a scalar result.

• gr: A function to return (as a vector) the gradient for those methods that can use this information.

  If 'gr' is NULL, a finite-difference approximation will be used. An open question concerns whether the SAME approximation code used for all methods, or whether there are differences that could/should be examined?

• lower, upper: Bounds on the variables for methods such as "L-BFGS-B" that can handle box (or bounds) constraints.

• method: A character string giving the name of the optimization method to be applied. See the list allmeth in file ctrldefault.R which is part of this package.

• hessian: A logical control that if TRUE forces the computation of an approximation to the Hessian at the final set of parameters. If FALSE (default), the hessian is calculated if needed to provide the KKT optimality tests (see kkt in Details for the control list). This setting is provided primarily for compatibility with optim().

• control: A list of control parameters. See Details .

• ...: For optimx further arguments to be passed to fn

  and gr; otherwise, further arguments are not used.

Details

Note that arguments after ... must be matched exactly.

See optimr() for other details.

Returns

An array with one row per set of starting parameters. Each row contains:

• par: The best set of parameters found.

• value: The value of ‘fn’ corresponding to ‘par’.

• counts: A two-element integer vector giving the number of calls to ‘fn’ and ‘gr’ respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to ‘fn’ to compute a finite-difference approximation to the gradient.

• convergence: An integer code. ‘0’ indicates successful completion

• message: A character string giving any additional information returned by the optimizer, or ‘NULL’.

• hessian: Always NULL for this routine.

Source

See the manual pages for optim() and the packages the DESCRIPTION suggests.

Examples

fnR <- function (x, gs=100.0) 
{
    n <- length(x)
    x1 <- x[2:n]
    x2 <- x[1:(n - 1)]
    sum(gs * (x1 - x2^2)^2 + (1 - x2)^2)
}
grR <- function (x, gs=100.0) 
{
    n <- length(x)
    g <- rep(NA, n)
    g[1] <- 2 * (x[1] - 1) + 4*gs * x[1] * (x[1]^2 - x[2])
    if (n > 2) {
        ii <- 2:(n - 1)
        g[ii] <- 2 * (x[ii] - 1) + 4 * gs * x[ii] * (x[ii]^2 - x[ii + 
            1]) + 2 * gs * (x[ii] - x[ii - 1]^2)
    }
    g[n] <- 2 * gs * (x[n] - x[n - 1]^2)
    g
}

pm <- rbind(rep(1,4), rep(pi, 4), rep(-2,4), rep(0,4), rep(20,4))
pm <- as.matrix(pm)
cat("multistart matrix:\n")
print(pm)

ans <- multistart(pm, fnR, grR, method="Rvmmin", control=list(trace=0))
ans