Use live parameters in sparse constraint Jacobians

[ChrisRackauckas-Claude]

Important

Ignore this PR until it has been reviewed by @ChrisRackauckas.

Summary

• accept the live parameter argument in generated and analytic sparse constraint-Jacobian callbacks
• rebuild DifferentiationInterface preparation when the live state or parameter type changes
• cover in-place/out-of-place and generated/analytic callbacks directly in OptimizationBase
• exercise generated and analytic sparse callbacks through OptimizationIpopt

Root cause

OptimizationIpopt switched to the generic OptimizationCache in #1257. That cache invokes constraint Jacobians with the current parameter value. The sparse instantiation path still produced two-argument callbacks that captured the initial parameter, causing a MethodError when called as cons_j(J, x, p). The out-of-place path had the equivalent missing live-parameter behavior.

This patch preserves the old two-argument convenience through default arguments while making the current parameter part of differentiation and analytic callback evaluation.

Investigation

• reproduced the failure from current master at be6fbd279
• traced the behavior change to Use the default OptimizationCache in OptimizationIpopt #1257; the same BoundaryValueDiffEq case passed with OptimizationIpopt 1.2.3
• reduced it to sparse generated and analytic constraint Jacobians
• added direct four-way coverage in OptimizationBase and an in-place solver integration test in OptimizationIpopt

Local validation

• OptimizationBase AD: 729 passed
• OptimizationIpopt Core: 129 passed, 1 pre-existing broken
• Runic check passed for all three changed Julia files
• git diff --check passed

[ChrisRackauckas-Claude]

Downstream confirmation from clean current SciML/BoundaryValueDiffEq.jl master (5e9eb4eff5e493c5ae56d5f4fc2027b446c55610).

I reduced lib/BoundaryValueDiffEqMIRK/test/Core/mirk_basic_tests.jl:597 to the vector-parameter TwoPointBVProblem solve with MIRK4(optimize = IpoptOptimizer()), then ran it in an isolated Julia 1.12 environment/depot.

Version boundary:

• OptimizationBase 5.2.1 + OptimizationIpopt 1.2.3: passes, p = [17.096586859834332]
• OptimizationBase 5.2.1 + OptimizationIpopt 1.3.0: fails in OptimizationIpopt.eval_constraint_jacobian because the generated sparse callback has only cons_j(J, x) but is called as cons_j(J, x, p)
• this PR's OptimizationBase at d1e327f4f + released OptimizationIpopt 1.3.0: passes, p = [17.096586859834332]

The 1.3.0 boundary maps to be6fbd279 / #1257. This PR is the correct upstream fix for the clean-main BoundaryValueDiffEq failure; no BVP-side test suppression or compatibility cap is needed.

[ChrisRackauckas-Claude]

Rebased onto current clean upstream/master (4d25faca8); new head 3961edfd6. Before the lease-protected push I audited the remote branch: it contained only the original ChrisRackauckas-Claude commit and no intervening contributor work. The rebased tree is byte-for-byte identical to the freshly validated tree. Current local verification: OptimizationBase AD 785/785; OptimizationBase Core 52/52; OptimizationIpopt 129 pass + 1 pre-existing broken; vector and immutable custom-SciMLStructures BoundaryValueDiffEqMIRK parameter-tuning solves both succeed with p = 17.096586859834332; Runic clean. Versioning remains intentionally untouched pending the merge/release ordering with #1287 and #1269.

[ChrisRackauckas-Claude]

CI triage after the clean-master rebase:

• The only non-systemic failure observed so far is downgrade OptimizationSophia. Its unseeded Lux/Sophia training assertion ended at 10 × objective = 4.4186e6 versus l1 = 3.5403e6.
• The simultaneous Recognize explicit second-order AutoSparse AD #1269 job on the same base passed OptimizationSophia 3/3, and the current master downgrade job also passes it.
• This PR only changes sparse DifferentiationInterface constraint-Jacobian construction; the Sophia test uses dense AutoZygote, so it does not execute the changed path.
• The remaining QA reexport failures reproduce on master and are already addressed by [AI] Curate the public API instead of blanket-reexporting dependencies #1286.

The available Actions credentials return 403 for a job rerun, so I could not request a clean retry.