dfoptim (version 2011.7-2)

nmk: A Nelder-Mead optimziation algorithm for derivative-free optimization

Description

An implementation of the Nelder-Mead algorithm for derivative-free optimization. This implementation is based on the Matlab code of Prof. C.T. Kelley (with his permission). It generally has better convergence than the Nelder-Mead implemenation in optim. Nelder-Mead is not recommended for high-dimensional (> 20 parameters) optimization problems.

Usage

nmk(par, fn, control = list(), ...)

Value

A list with the following components:parBest estimate of the parameter vector found by the algorithm.valueThe value of the objective function at termination.fevalThe number of times the objective fn was evaluated.restartsThe number of times the algorithm had to be restarted when it stagnated.convergenceAn integer code indicating type of convergence. 0 indicates successful convergence. Positive integer codes indicate failure to converge.messageText message indicating the type of convergence or failure.

Details

Argument control is a list specifing any changes to default values of algorithm control parameters for the outer loop. Note that the names of these must be specified completely. Partial matching will not work. The list items are as follows: tol Convergence tolerance. Iteration is terminated when the absolute difference in function value between successive iteration is below tol. Default is 1.e-06. maxfeval: Maximum number of objective function evaluations allowed. Default is min(5000, max(1500, 20*length(par)^2)). regsimp A logical variable indicating whether the starting parameter configuration is a regular simplex. Default is TRUE. maximize A logical variable indicating whether the objective function should be maximized. Default is FALSE. restarts.max Maximum number of times the algorithm should be restarted before declaring failure. Default is 3. trace A logical variable indicating whether the starting parameter configuration is a regular simplex. Default is FALSE.

References

C.T. Kelley (1999), Iterative Methods for Optimization, SIAM.

See Also

optim

Examples

rosbkext <- function(x){
# Extended Rosenbrock function
 n <- length(x)
 sum (100*(x[1:(n-1)]^2 - x[2:n])^2 + (x[1:(n-1)] - 1)^2)
 }

np <- 10
set.seed(123)

p0 <- rnorm(np)
xm1 <- nmk(fn=rosbkext, par=p0) # maximum `fevals' is not sufficient to find correct minimum
xm2 <- nmk(fn=rosbkext, par=p0, control=list(maxfeval=5000)) # finds the correct minimum 
xm3 <- nmk(fn=rosbkext, par=p0, control=list(regsimp=FALSE, maxfeval=5000)) # also finds the correct minimum 

ans.optim <- optim(fn=rosbkext, par=p0, method="Nelder-Mead", control=list(maxit=5000))   # terminates with inferior estimates

### A non-smooth problem
nsf <- function(x) {
	f1 <- x[1]^2 + x[2]^2
	f2 <- x[1]^2 + x[2]^2 + 10 * (-4*x[1] - x[2] + 4)
	f3 <- x[1]^2 + x[2]^2 + 10 * (-x[1] - 2*x[2] + 6)
	max(f1, f2, f3)
}

p0 <- rnorm(2)
xm4 <- nmk(fn=nsf, par=p0)