[R] Relatively Simple Maximization Using Optim Doesnt Optimize

[Abby Spurdle]

I'm sorry, Duncan.
But I disagree.

This is not a "bug" in optim function, as such.
(Or at least, there's nothing in this discussion to suggest that there's a bug).
But rather a floating point arithmetic related problem.

The OP's function looks simple enough, at first glance.
But it's not.

Plotting a numerical approximation of the derivative, makes the
problem more apparent:
----------
plot_derivative <- function (f, a = sol - offset, b = sol + offset,
sol, offset=0.001, N=200)
{   FIRST <- 1:(N - 2)
    LAST <- 3:N
    MP <- 2:(N - 1)

    x <- seq (a, b, length.out=N)
    y <- f (x)
    dy <- (y [LAST] - y [FIRST]) / (x [LAST] - x [FIRST])

    plot (x [MP], dy, type="l", xlab="x", ylab="dy/dx (approx)")
}

optim.sol <- optim (1001, production1 ,method="CG", control = list
(fnscale=-1) )$par
plot_derivative (production1, sol=optim.sol)
abline (v=optim.sol, lty=2, col="grey")
----------

So, I would say the optim function (including the CG method) is doing
what it's supposed to do.

And collating/expanding on Nash's, Jeff's and Eric's comments:
(1) An exact solution can be derived quickly, so using a numerical
method is unnecessary, and inefficient.
(2) Possible problems with the CG method are noted in the documentation.
(3) Numerical approximations of the function's derivative need to be
well-behaved for gradient-based numerical methods to work properly.


On Fri, Mar 13, 2020 at 3:42 AM Duncan Murdoch <murdoch.duncan using gmail.com> wrote:
>
> It looks like a bug in the CG method.  The other methods in optim() all
> work fine.  CG is documented to be a good choice in high dimensions; why
> did you choose it for a 1 dim problem?
>
> Duncan Murdoch