Dealing with bound_relax_factor

[dallan-keylogic]

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Repeatedly, IPOPT and AMPL cause problems with certain functions for which function evaluation errors are possible (fractional powers, logs, etc). Fortunately, we have display_potential_evaluation_errors in order to avoid these situations. However, even if the user has properly bounded these functions below by zero (or some eps>0), we can still run into problems because IPOPT has the option bound_relax_factor set to 1e-8 by default. I even got caught off-guard today because I bounded a variable below by 1e-7, but that value was transformed to 1e-11 when the Pyomo scaling transformation was applied.

There are two options to deal with this problem:

1. Set the default option bound_relax_factor=0 in the IDAES solver config.
2. Update display_potential_evaluation_errors to not just evaluation errors, but also near-evaluation errors.

Option (2) is probably what we'll end up doing. It would be nice to have some discussion, though.

[michaelbynum]

I agree that (2) is probably preferable. However, I think the primary motivation for the bound relaxation is to ensure there is a strict interior to the feasible region. This most often is needed when the lower and upper bounds of a variable are too close (e.g., equal). I think that the presolve in the NL writer should now catch and resolve a lot of these situations, so option (1) might not be a bad idea. Having said all that, I would still favor option (2). Thoughts, @jsiirola?

[adam-a-a]

Not sure if this will be of use, but @bknueven had done some work that involved tweaking bound_relax_factor for ipopt-watertap, which now lives here: https://github.com/watertap-org/watertap-solvers/blob/main/src/watertap_solvers/_base.py

From one of the older PRs: https://github.com/watertap-org/watertap-solvers/commit/343b99b6794e1d49c4918452ace776e2292e177b

[bknueven]

Here is the original PR: https://github.com/watertap-org/watertap/pull/1162. We've had bound_relax_factor turned off in WaterTAP for over a year without issue, as far as I am aware. Users typically explicitly fix the variable if that's what they want. Variables fixed implicitly through bounds and not through a constraint or by calling fix also make the degrees of freedom calculation incorrect, so I imagine it should generally be avoided.

Often times in WaterTAP we wanted a strict inequality anyways, which is what bound_relax_factor == 0 essentially gets you. We had to modify a few bounds on variables as a result in a few places in the codebase, but the number of changes overall was small considering the number of models WaterTAP hosts.

[michaelbynum]

That is super helpful. Thanks @bknueven and @adam-a-a!

[michaelbynum]

So we probably want to implement option (1). However, option (2) could also be useful.

[dallan-keylogic]

Another thought is to look for possible singularities not just in function evaluations, but also their derivatives. That might be too complex, however.