ljoptim function

(Adaptive) Version of Luus-Jaakola Optimization

Adaptive means that the search space reduction factors in the number of iterations; makes convergence faster at about 100 iterations

ljoptim(
  x,
  fun,
  ...,
  red = ifelse(adaptive, 0.99, 0.95),
  lower,
  upper,
  acc = 1e-06,
  accd = 1e-04,
  itmax = 1000,
  verbose = 0,
  adaptive = TRUE
)

Arguments

• x: optional starting values
• fun: function to minimize
• ...: additional arguments to be passed to the function to be optimized
• red: value of the reduction of the search region
• lower: The lower contraints of the search region
• upper: The upper contraints of the search region
• acc: if the numerical accuracy of two successive target function values is below this, stop the optimization; defaults to 1e-6
• accd: if the width of the search space is below this, stop the optimization; defaults to 1e-4
• itmax: maximum number of iterations
• verbose: numeric value hat prints information on the fitting process; >2 is extremely verbose
• adaptive: should the adaptive version be used? defaults to TRUE.

Returns

A list with the components (optim)

• par The position of the optimimum in the search space (parameters that minimize the function; argmin fun)
• value The value of the objective function at the optimum (min fun)
• counts The number of iterations performed at convergence with entries fnction for the number of iterations and gradient which is always NA at the moment
• convergence 0 successful completion by the accd or acc criterion, 1 indicate iteration limit was reached, 99 is a problem
• message is NULL (only for compatibility or future use)

Examples

fbana <- function(x) {
x1 <- x[1]
x2 <- x[2]
100 * (x2 - x1 * x1)^2 + (1 - x1)^2
}
res1<-ljoptim(c(-1.2,1),fbana,lower=-5,upper=5,accd=1e-16,acc=1e-16)
res1

set.seed(210485)
fwild <- function (x) 10*sin(0.3*x)*sin(1.3*x^2) + 0.00001*x^4 + 0.2*x+80
plot(fwild, -50, 50, n = 1000, main = "ljoptim() minimising 'wild function'")
res2<-ljoptim(50, fwild,lower=-50,upper=50,adaptive=FALSE,accd=1e-16,acc=1e-16)
points(res2$par,res2$value,col="red",pch=19)
res2