[R-sig-ME] Optimize multiple confounded parameters using optim()

[Keren Halabi]

Dear list,

My apologies in advance if this is not the relevant forum for the below
question.

I wish to define a codon site model, which is mixture model over multiple
dN/dS ratios.
Thus, I want to constrain each  dN/dS ratio by its preceding ratio in the
mixture and its following ratio in the mixture. I was thinking of using the
bounds parameter of the optim() function to achieve this.

However, I am experiencing an issue while attempting to optimize a function
with regards to multiple parameters. Specifically, due to setting the
bounds to be dependent on one another.

Here is a basic example: say that I want to optimize the below function
named "test', with regards to vector v, with the following constraint:
0<=v[1]<=v[2]<=1:
test <-function(v=c(0,1)) {return(v[2]-v[1])}

Now, calling optim() with the following settings:
a=0
b=1
res = optim(c(a,b), test, lower=c(0,a), upper=c(b,1),method="L-BFGS-B")

Yields optimized values:
a=1
b=0
test(c(a,b))=-1

It appears that the constraint was not satisfied, but the bounds still had
some  affect on the result. This makes me suspect that I didn't set the
lower and upper bounds correctly when calling optim().
Could you please let me know what I did wrong?

Many thanks!
Keren

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