[R] nlm question

[Laura Holt]

Dear R People:

I am trying to duplicate the example from Dennis and Schnabel's "Numerical 
Methods for Unconstrained Optimization and Nonlinear Equations", which 
starts on page 149.

My reason for doing so:  to try to understand the "nlm" function.

Here is the function:
>mfun1
function(x) {
        z <- matrix(0,nrow=2,ncol=1)
        z[1,1] <- x[1]^2 + x[2]^2 - 2
        z[2,1] <- exp(x[1]-1) + x[2]^3 - 2
        res <- 0.5*t(z)%*%z
        res
}

This function has a root at c(1,1).
When I use the following:
>nlm(mfun1,c(2,0.5))
$minimum
[1] 0.09168083

$estimate
[1]  1.485078e+00 -4.973395e-07

$gradient
[1] -8.120649e-09  1.096345e-09

$code
[1] 1

$iterations
[1] 19

I get the solution of 1.485078 and zero.

Now when I use:
>nlm(mfun1,c(1.2,0.85))
$minimum
[1] 2.025965e-12

$estimate
[1] 1.000001 0.999999

$gradient
[1] 6.799786e-08 6.520232e-08

$code
[1] 1

$iterations
[1] 8

>
I get the appropriate answer.

What can I put into my code to improve the estimates, please?

Thanks
Sincerely,
Laura Holt
R Version 2.0.0
Windows
mailto: lauraholt_938 at hotmail.com