[R] The best solver for non-smooth functions?

[Hans W Borchers]

Cren <oscar.soppelsa <at> bancaakros.it> writes:
>

The most robust solver for non-smooth functions I know of in R is Nelder-Mead 
in the 'dfoptim' package (that also allows for box constraints).

First throw out the equality constraint by using c(w1, w1, 1-w1-w2) as input. 
This will enlarge the domain a bit, but comes out allright in the end.

    sharpe2 <- function(w) {
    	w <- c(w[1], w[2], 1-w[1]-w[2])
      - (t(w) %*% y) / cm.CVaR(M, lgd, w, N, n, r, rho, alpha, rating)
    }
    
    nmkb(c(1/3,1/3), sharpe2, lower=c(0,0), upper=c(1,1))
    ## $par
    ## [1] 0.1425304 0.1425646
    ## $value
    ## [1] -0.03093439

This is still in the domain of definition, and is about the same optimum that 
solnp() finds.

There are some more solvers, especially aimed at non-smooth functions, in the 
making. For low-dimensional problems like this Nelder-Mead is a reasonable 
choice.


> # Whoops! I have just seen there's a little mistake
> # in the 'sharpe' function, because I had to use
> # 'w' array instead of 'ead' in the cm.CVaR function!
> # This does not change the main features of my,
> # but you should be aware of it
> 
> ---
> 
> # The function to be minimized
> 
> sharpe <- function(w) {
>   - (t(w) %*% y) / cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)
> } 
> 
> # This becomes...
> 
> sharpe <- function(w) {
>   - (t(w) %*% y) / cm.CVaR(M, lgd, w, N, n, r, rho, alpha, rating)
> } 
> 
> # ...substituting 'ead' with 'w'.
>