appsi_highs: allow solving quadratic problems

[maurerle]

Fixes #3381.

Summary/Motivation:

Before, the highs solver did not allow to solve quadratic equations, but highs does support solving such.
I did only run a few test cases which are solved by using this.
This was added 3 years ago with the appsi_highs solver, though a lot happened in highs in the meantime.

Changes proposed in this PR:

• remove highs restriction to disable solving quadratic equations

Legal Acknowledgement

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Tested with:

• debian 13 trixie
• highspy 1.7.2
• pyomo derived from main

[jsiirola]

Thank you for your interest in getting QP support added to the HiGHS interface, Unfortunately just removing the guard against nonlinear constraints and objectives doesn't actually pass the nonlinear terms on to HiGHS. For this PR to be accepted, it will need significant rework to (at a minimum):

• add the logic for passing the quadratic terms from the compiled representation to the HiGHS solver
• update tests to exercise the logic using QPs with known solutions (possibly sufficient to add HiGHS to the standard solver tests for solvers that support (QC)QPs

Given the significant amount of work that will need to be incorporated in this before the PR can be merged, I would suggest closing this PR and re-opening when it is (closer to) complete.

[maurerle]

This is indeed much more complex. If someone hints me how I can improve my draft, I would be happy to do so, but fro now, I will close this :)

[jsiirola]

I did a little digging, so maybe some of this will be helpful:

• HiGHS only supports QPs, so you only want to turn on processing for quadratic terms when handling the objective (and not for constraints)
• I believe the method you want to use to pass the quadratic coefficients in to HiGHS is passHessian
• We don't have quite the same general testing framework for APPSI that exists for the legacy solvers. In particular, there is no category for "MIQP solvers" (only QCQP and MIQCQP). You might be able to tie into the legacy solver tests through APPSI's legacy interface, or extend the APPSI test framework to include tests for (MI)QPs. This is likely to be involved. You should also be aware of current work building a new standard for Pyomo solver interfaces (to replace both the legacy interface and APPSI). This effort will almost certainly overhaul the infrastructure for testing the solvers using a standard test suite. It might be worth waiting until that effort is farther along (hopefully tings will look close in a month or 2).
• Hopefully @michaelbynum can weigh in on any general strategies you should consider when determining what needs to be cached to support efficient model updates, and how those caches should integrate into the rest of the APPSI infrastructure.