% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/mlsl.R
\name{mlsl}
\alias{mlsl}
\title{Multi-level Single-linkage}
\usage{
mlsl(x0, fn, gr = NULL, lower, upper, local.method = "LBFGS",
  low.discrepancy = TRUE, nl.info = FALSE, control = list(), ...)
}
\arguments{
\item{x0}{initial point for searching the optimum.}

\item{fn}{objective function that is to be minimized.}

\item{gr}{gradient of function \code{fn}; will be calculated numerically if
not specified.}

\item{lower, upper}{lower and upper bound constraints.}

\item{local.method}{only \code{BFGS} for the moment.}

\item{low.discrepancy}{logical; shall a low discrepancy variation be used.}

\item{nl.info}{logical; shall the original NLopt info been shown.}

\item{control}{list of options, see \code{nl.opts} for help.}

\item{...}{additional arguments passed to the function.}
}
\value{
List with components:
  \item{par}{the optimal solution found so far.}
  \item{value}{the function value corresponding to \code{par}.}
  \item{iter}{number of (outer) iterations, see \code{maxeval}.}
  \item{convergence}{integer code indicating successful completion (> 0)
    or a possible error number (< 0).}
  \item{message}{character string produced by NLopt and giving additional
    information.}
}
\description{
The ``Multi-Level Single-Linkage'' (MLSL) algorithm for global optimization
searches by a sequence of local optimizations from random starting points.
A modification of MLSL is included using a low-discrepancy sequence (LDS)
instead of pseudorandom numbers.
}
\details{
MLSL is a `multistart' algorithm: it works by doing a sequence of local
optimizations (using some other local optimization algorithm) from random or
low-discrepancy starting points.  MLSL is distinguished, however by a
`clustering' heuristic that helps it to avoid repeated searches of the same
local optima, and has some theoretical guarantees of finding all local
optima in a finite number of local minimizations.

The local-search portion of MLSL can use any of the other algorithms in
NLopt, and in particular can use either gradient-based or derivative-free
algorithms.  For this wrapper only gradient-based \code{L-BFGS} is available
as local method.
}
\note{
If you don't set a stopping tolerance for your local-optimization
algorithm, MLSL defaults to \code{ftol_rel=1e-15} and \code{xtol_rel=1e-7}
for the local searches.
}
\examples{

### Minimize the Hartmann6 function
hartmann6 <- function(x) {
    n <- length(x)
    a <- c(1.0, 1.2, 3.0, 3.2)
    A <- matrix(c(10.0,  0.05, 3.0, 17.0,
                   3.0, 10.0,  3.5,  8.0,
                  17.0, 17.0,  1.7,  0.05,
                   3.5,  0.1, 10.0, 10.0,
                   1.7,  8.0, 17.0,  0.1,
                   8.0, 14.0,  8.0, 14.0), nrow=4, ncol=6)
    B  <- matrix(c(.1312,.2329,.2348,.4047,
                   .1696,.4135,.1451,.8828,
                   .5569,.8307,.3522,.8732,
                   .0124,.3736,.2883,.5743,
                   .8283,.1004,.3047,.1091,
                   .5886,.9991,.6650,.0381), nrow=4, ncol=6)
    fun <- 0.0
    for (i in 1:4) {
        fun <- fun - a[i] * exp(-sum(A[i,]*(x-B[i,])^2))
    }
    return(fun)
}
S <- mlsl(x0 = rep(0, 6), hartmann6, lower = rep(0,6), upper = rep(1,6),
            nl.info = TRUE, control=list(xtol_rel=1e-8, maxeval=1000))
## Number of Iterations....: 1000
## Termination conditions:
##   stopval: -Inf, xtol_rel: 1e-08, maxeval: 1000, ftol_rel: 0, ftol_abs: 0
## Number of inequality constraints:  0
## Number of equality constraints:    0
## Current value of objective function:  -3.32236801141552
## Current value of controls:
##   0.2016895 0.1500107 0.476874 0.2753324 0.3116516 0.6573005

}
\references{
A. H. G. Rinnooy Kan and G. T. Timmer, ``Stochastic global
optimization methods'' Mathematical Programming, vol. 39, p. 27-78 (1987).

Sergei Kucherenko and Yury Sytsko, ``Application of deterministic
low-discrepancy sequences in global optimization,'' Computational
Optimization and Applications, vol. 30, p. 297-318 (2005).
}
\seealso{
\code{\link{direct}}
}
\author{
Hans W. Borchers
}