Move OA selection to mip-nlp solver

[bernalde]

Summary

Closes #319.

This moves OA selection toward the solver-family API described in the issue:

• adds solver="mip-nlp" as a first-class MINLP decomposition selector
• adds mip_nlp_method / mip_nlp_options
• routes mip_nlp_method="oa" and "ecp" through the existing OA implementation
• keeps gdp_method="oa" as a deprecation-warning compatibility alias
• leaves gdp_method to describe GDP reformulation choices for the new route

The broader MindtPy-style methods (goa, roa, fp, lp_nlp_bb) are reserved by name and raise NotImplementedError until they are implemented.

Validation

• PYTHONPATH=python python -m ruff check python/discopt/solvers/mip_nlp.py python/discopt/solver.py python/discopt/modeling/core.py python/tests/test_mip_nlp.py python/tests/test_oa.py
• PYTHONPATH=python pytest python/tests/test_mip_nlp.py python/tests/test_oa.py -q

Note: local commit hooks were skipped because pre-commit is not installed in this environment; the targeted Ruff and pytest checks above pass.

[jkitchin]

A review highlighted:

3. python/discopt/solver.py (new mip-nlp route, ~2400) — GDP-reformulation asymmetry between the two "equivalent" OA routes.
   The new solver="mip-nlp" route calls reformulate_gdp(model, method="big-m") before solving, but the deprecated gdp_method="oa" alias does not reformulate (it calls solve_mip_nlp on the raw model, matching the old solve_oa path). So for a model containing disjunctions, the documented-as-equivalent old and new routes produce materially different problems. Worth either reformulating in both routes or documenting that the deprecated alias deliberately preserves the no-reformulation legacy behavior. (reformulate_gdp is a no-op when no GDP constraints exist, so models without disjunctions — including all the new tests — are unaffected, which is why this slipped past the suite.)

Notes (not blocking)
The mip-nlp route warns only about leftover **kwargs; named solve_model options it ignores (e.g. threads, strategy, skip_convex_check) are dropped silently, unlike the AMP route which explicitly enumerates ignored named options. Minor consistency gap.

Can you take a look and let me know when you think this is ready to merge?

[bernalde]

Commits pushed:

• f5e57df Address mip-nlp GDP routing review

Main changes:

• Made the deprecated gdp_method="oa" alias reformulate GDP models with big-m before dispatching to solve_mip_nlp, matching the explicit solver="mip-nlp", mip_nlp_method="oa" route.
• Updated the deprecation warning to say that gdp_method="oa" is interpreted as big-m for GDP reformulation in this compatibility path.
• Added MIP-NLP warnings for non-default named solve_model options that the route ignores, including threads, strategy, and skip_convex_check.
• Added a regression test covering GDP reformulation for both the new MIP-NLP route and the deprecated OA alias.

Tests run:

• PYTHONPATH=python pytest python/tests/test_mip_nlp.py::test_mip_nlp_and_deprecated_oa_alias_reformulate_gdp -q failed before the fix, then passed after.
• PYTHONPATH=python pytest python/tests/test_mip_nlp.py -q: 5 passed.
• PYTHONPATH=python python -m ruff format --check python/discopt/solver.py python/tests/test_mip_nlp.py: passed.
• PYTHONPATH=python python -m ruff check python/discopt/solver.py python/tests/test_mip_nlp.py: passed.
• PYTHONPATH=python python -m mypy python/discopt/solver.py python/tests/test_mip_nlp.py: passed.
• PYTHONPATH=python pytest python/tests/test_mip_nlp.py python/tests/test_oa.py -q: 12 passed.
• PYTHONPATH=python pytest python/tests/test_mip_nlp.py python/tests/test_gdp.py python/tests/test_oa.py -q: 114 passed, 22 deselected.

Comments intentionally not addressed:

• None.

Remaining risks or follow-up:

• This keeps the MIP-NLP route on the explicit GDP-to-MIP reformulation path. Native disjunctive or logic-based GDP handling should remain a separate solver/design path rather than being implied by this OA compatibility alias.

[bernalde]

@jkitchin One deeper design question from #319 that I think is worth settling before we build further on this API: should discopt treat disjunctive solvers as a separate axis from MIP/MINLP solvers?

My current mental model is:

• gdp_method should answer how a disjunctive model is handled: either reformulate disjunctions into an algebraic MIP/MINLP with big-m, hull, mbigm, or auto, or solve the disjunctive form natively with a logic-based method.
• solver / mip_nlp_method should answer how the resulting algebraic MIP/MINLP is solved. OA belongs in this category in general: it is a MIP-NLP decomposition method, although the same OA idea can be generalized to disjunctive programs as logic-based OA.
• Logic-based OA for GDPs should probably live with native disjunctive solving, not as a GDP reformulation option.

This PR chooses the reformulation path for the deprecated alias: gdp_method="oa" means OA solver selection plus big-m GDP reformulation for compatibility. Does that match how you want to separate these axes long term, or would you prefer a different naming split for native disjunctive solvers?

[jkitchin]

Agreed on the two-axis split — that's the contract we'll build on, and I've merged this PR since it's correct and unblocks the API.

• gdp_method = how a disjunctive model is handled: reformulate to algebraic MIP/MINLP (big-m, hull, mbigm, auto) or solve the disjunctive form natively (logic-based methods).
• solver / mip_nlp_method = how the resulting algebraic MIP/MINLP is solved (OA, ECP, and the reserved goa/roa/fp/lp_nlp_bb).

The native axis already lives on gdp_method today, which is the proof that this split is the existing convention rather than a new one: gdp_method="loa" dispatches to solve_gdpopt_loa (solver.py:2699). So logic-based OA is already a native-disjunctive option, not a mip_nlp_method. This PR's deprecated gdp_method="oa" → "OA solver + big-M reformulation" is consistent with that — it's reformulation + algebraic OA, not native solving.

Two decisions we'll treat as the agreed contract for follow-ups:

1. Native + mip-nlp ⇒ raise. A native-disjunctive gdp_method (e.g. loa) combined with solver="mip-nlp" is contradictory (one says "solve natively," the other "reformulate to algebraic and decompose"), so it should raise rather than silently reformulate.
2. goa ≠ gloa. goa stays a mip_nlp_method (generalized/global OA on the algebraic MINLP); global logic-based OA (gloa) belongs on the native-disjunctive axis under gdp_method. They must not be aliased to each other.

Captured both in #323 so they aren't lost. Thanks for pushing on the design here.

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