I have a convex objective function that I want to minimize (unconstrained). It depends ~ 200 variables. I’m running Optim on it, but it takes forever (has been computing for a full day now).

I want to improve the performance of this, if it is possible. First I would like to know the time that Optim typically would require on problems of this scale (hundreds of variables), so that I have a reference point.

Next, I would like to know what factors could be the main bottlenecks when using Optim, so that I can look in my code and see if I can fix them.

Other than that, are there any alternative good libraries for convex minimization (unconstrained) with a large number of variables?