Different numerical linear algebra and numerical optimization methods have different size regimes where they're a 'good idea', in addition to their own properties. For example, for very large optimization problems, gradient, stochastic gradient and coordinate descent methods are used instead of Newton or Interior Point methods because you don't have to deal with the Hessian. Similarly, dense linear solver methods stop being feasible after a certain size.
So given that both the algorithms and the computer hardware are changing constantly, what's a good way to know, and keep up with, how big is too big for standard linear algebra and optimization solvers?
(I'm thinking about this because when you're an end-user of numerics algorithms it's important to have a vague idea when those algorithms can be applied. Part of that is problem structure and the sort of solution desired, but part of it is also just the size of the problem.)
EDIT: For more concreteness, what got me thinking about this was varying rules of thumb on the upper bounds for how large a problem interior point algorithms could solve. Earlier papers said the dimensionality should be around 1000 while later papers had revised upwards to 5000 and even more recent papers allow for even larger depending on if you can take advantage of sparsity. That's a rather large range, so I'm curious what is large for state of the art interior point methods.