Get number of iterations after optimization

[ojwoodford]

It would be great to have a way to retrieve the number of iterations that Ipopt performed during an optimization. This can be useful to understand whether a particular cost function is either slow to evaluate or slow to converge. It can also be used to have a more fine-grained comparison between optimizers.

[odow]

This is not implemented because Ipopt does not provide a nice way of accessing after a solve.

The recommended alternative is to write a solver-specific callback:
https://github.com/jump-dev/Ipopt.jl#solver-specific-callbacks

I don't know if the iteration could is a reasonable comparison between solvers. Ipopt may use multiple functions evaluations per iteration.

To debug a solve, you generally need to look at the log and see how the barrier is progressing. It isn't as simple as a metric like iterations/second.

Is this so you can compare with NNLS?

[ojwoodford]

Is this so you can compare with NNLS?

So I can compare with other solvers on non-linear least squares problems, yes.

I can see the number of iterations in the log. It's pretty comparable with other methods. It's always useful to see how much work a particular solver is able to do per "iteration", whatever that happens to mean in the context of a particular solver.

[odow]

See #389