hillclimbing <- function ( f, x, h = 1.0, m = 1000 )

#*****************************************************************************80
#
## hillclimbing minimizes a multivariate function using hill climbing.
#
#  Licensing:
#
#    Copyright 2016 James P. Howard, II
#
#    The computer code and data files on this web page are distributed under
#    https://opensource.org/licenses/BSD-2-Clause, the BSD-2-Clause license.
#
#  Modified:
#
#    17 March 2020
#
#  Author:
#
#    Original R code by James Howard;
#    Modifications by John Burkardt.
#
#  Reference:
#
#    James Howard,
#    Computational Methods for Numerical Analysis with R,
#    CRC Press, 2017,
#    ISBN13: 978-1-4987-2363-3.
#
{
  n <- length ( x )
  xcurr <- x
  ycurr <- f ( x )

  for ( j in 1 : m )
  {
    xnext <- xcurr
    i <- ceiling ( runif ( 1, 0, n ) )
    xnext[i] <- rnorm ( 1, xcurr[i], h )
    ynext <- f ( xnext )
    if ( ynext < ycurr )
    {
      xcurr <- xnext
      ycurr <- ynext
    }
  }

  x <- xcurr

  return ( x )
}