Optimization with constraints via parameter transform

constrainOptim.R

#############################################################
# Optimization with constraints via parameter transform
# Sean Wu
#############################################################

# same as qlogis
logit <- function(x){
  log(x/(1-x))
}

# same as plogis
invlogit <- function(x){
  exp(x)/(1+exp(x))
}

# our target function to optimize; it has global minimum at x = 0 for all dimensions
griewank <- function(xx){
  xx <- invlogit(xx) # constrain all parameters to lie between 0,1
  if(any(xx > 1 | xx < 0)){
    stop("transformed parameters lie outside [0,1]")
  }
  ii <- c(1:length(xx))
  sum <- sum(xx^2/4000)
  prod <- prod(cos(xx/sqrt(ii)))

  y <- sum - prod + 1
  return(y)
}

optimOut = optim(par = invlogit(c(-5,5)),fn = griewank,method = "Nelder-Mead")
invlogit(optimOut$par) # the real global minima is at 0,0; it's very small here, just as we would expect