# [S] Optimization problem

Fri, 31 Jul 1998 18:02:27 -0300

Dear S users,

I am trying to find the optimum of a function:

I have the following function which I want to fine your minimum:

ob<-
function(alpha, beta)
{
(-1 * (N * log(alpha) + (N * alpha - 1) * log(beta) - (alpha - 1) *
sum(log(beta + x))))/N
}

I have also the gradient and hessian matrix in the list:

function(alpha, beta)
{
list(gradient = c(-1/alpha - log(beta) + sum(log(beta + x))/N, - (N *
alpha - 1)/(N * beta) + ((alpha
+
1) * sum(1/(beta + x)))/N), hessian = c(1/(alpha^2), -1/beta +
sum(1/(beta - x))/N, (N * alpha
-
1)/(N * beta^2) - ((alpha + 1) * sum(1/((beta + x)^2)))/N))
}

WHERE: 0<alpha<1
0<beta<infinity
M=52 and N=30 (both avaliable in working directory)
x=c(49, 5, 17, 2, 39, 84, 7, 0, 35, 36, 1400, 5, 34, 15,
11, 2, 1, 39, 8, 101, 2, 148, 1, 68,
31, 1, 20, 118, 91, 427) (avaliable in working
directory)

So, I put the command:

nlminb(st = c(0.4, 5), objective = ob, gradient = grad, hessian = T, ,
N = N, M = M, x = x)

\$parameters:
[1] 0.4 5.0

\$objective:
[1] 0

\$message:
NULL

[1] 0

\$iterations:
[1] 0

\$f.evals:
[1] 1

\$g.evals:
[1] 1

\$hessian:
[,1] [,2]
[1,] 0 0
[2,] 0 0

\$scale:
[1] 1 1

\$aux:
\$aux\$N:
[1] 30

\$aux\$M:
[1] 52

\$aux\$x:
[1] 49 5 17 2 39 84 7 0 35 36 1400 5 34
15 11 2 1 39 8 101 2
[22] 148 1 68 31 1 20 118 91 427

\$call:
nlminb(start = c(0.4, 5), objective = ob, gradient = grad, hessian = T,
N = N, M = M, x = x)

Warning messages:
1: Condition has 2 elements: only the first used in: is.na(fx) ||
is.nan(fx)
2: singularity encountered in: nlminb.2(temp, p, liv, lv, lh, objective,