Summary/Motivation:

One advantage of using CyIpopt over Ipopt is the ability to interact with the solver via a callback. Another advantage is that we can associate the solver's data structures with Pyomo variables and constraints, which might have more meaning for a user. This PR combines these capabilities by introducing a callback that displays the variables and constraints that correspond to the highest-magnitude infeasibilities each iteration of a solve.

This PR will not work until CyIpopt publishes a new release, but I wanted to open it for feedback and possibly solicit some ambitious users.

This PR needs:

• Unit tests (capture output and make sure it is as expected)
• Practical testing debugging real problems
• CyIpopt release

Ideally, eventually, we could automatically link CyIpopt to the IDAES-provided Ipopt library, so that users can obtain this functionality with a simple pip install cyipopt. Then I envision the callback being enabled with something like

solver = pyo.SolverFactory("cyipopt")
solver.options["infeasibility_callback"] = True

Breaking change

Note that this is a breaking change to the call signature of the intermediate callback that our CyIpopt interface, CyIpoptNLP, expects. We now expect an argument for self, the instance of cyipopt.Problem, which is necessary for calling the get_current_iterate and get_current_violations methods. We could think about how to do this in a non-breaking manner (using inspect to branch on the signature of the callback) or how to update the signature to be more extensible (accept a dictionary as an argument that we can add to if/when ever we want to add more arguments to the callback).

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