[R] Relatively Simple Maximization Using Optim Doesnt Optimize

[Gabor Grothendieck]

It seems CG is having problems with the cube root.  This converges while
still using CG:

S1 <- optim(1001,function(x) (production1(x)^3), method = "CG",
  control = list(fnscale=-1))

On Thu, Mar 12, 2020 at 9:34 AM Skyler Saleebyan
<skylerbsaleebyan using gmail.com> wrote:
>
> I am trying to familiarize myself with optim() with a relatively simple
> maximization.
>
> Description:
> L and K are two terms which are constrained to add up to a total 100000
> (with respective weights to each). To map this constraint I plugged K into
> the function (to make this as simple as possible.)
>
> Together these two feed into one nonlinear function which is the product of
> two monotonic (on the positive interval) functions. Then that numbers is
> returned in a function fed to optim, which should maximize the output by
> adjusting L. The whole code is:
>
> production1 <- function(L){
>   budget=100000
>   Lcost=12
>   Kcost=15
>   K=(budget-L*Lcost)/Kcost
>   machines=0.05*L^(2/3)*K^(1/3)
>   return(machines)
> }
>
> # production1(6000) #example of number with much higher output vs optim
> result
> S1=optim(1001,production1,method="CG",control=list(fnscale=-1))
> S1
>
> Output:
> $par
> [1] 1006.536
>
> $value
> [1] 90.54671
>
> $counts
> function gradient
>      201      101
>
> $convergence
> [1] 1
>
> $message
> NULL
>
>
> For some reason this never explores the problem space and just spits out
> some answer close to the initial condition. What am I doing wrong?
>
> Thanks,
> Skyler S.
>
>         [[alternative HTML version deleted]]
>
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