Cap AutoEnzyme Lagrangian Hessian batches at width 8

[ChrisRackauckas-Claude]

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

What changed and why

OptimizationBase now computes generated AutoEnzyme Lagrangian Hessians in batches capped at width 8. Inputs larger than 8 use repeated fixed-width calls with zero tangent padding in the final batch, reusing the private policy and caches already used for objective Hessians.

OptimizationMOI requests lag_h for non-symbolic constrained problems. That path still differentiated every variable in one BatchDuplicated, so its LLVM compile time grew sharply with problem size even after objective Hessian batching was added in #1331. This change covers both dense and packed in-place Lagrangian Hessian outputs, is internal, and adds no public API or dependency.

Failing before and passing after

The same 17-parameter regression test computes and checks dense and packed Lagrangian Hessians, then verifies that the generated closure captures the width-8 policy.

Clean origin/master with the test applied:

Enzyme Hessian batch cap: Test Failed
Expression: any((getfield(optf_lagrangian.lag_h, i) isa Val{8} ...))
AD | 803 passed, 1 failed, 804 total in 9m06.1s

This branch:

AD | 804 passed / 804 total in 8m46.5s
Testing OptimizationBase tests passed
Testing Optimization tests passed

A focused Julia 1.11.9 reproducer using the exact 183-variable, 120-constraint clnlbeam equations loaded the OptimizationEnzymeExt path and checked its result against the analytic Hessian:

OptimizationBase 5.5.3, unbounded width: 207.182129194 seconds, max error 0.0
this branch, width 8:                  11.457115908 seconds, max error 0.0

The reduced three-backend benchmark sequence also discriminated the change:

OptimizationBase 5.5.3: exit 124 after 1:00:14, last line `start backend=enzyme N=60`
this branch: exit 0 after 6:40.57, correct objectives through the benchmark's time gating

Verification

GROUP=OptimizationBase_AD julia +1.12.7 --startup-file=no --project=. -e 'using Pkg; Pkg.test()'
AD | 804 passed / 804 total in 8m46.5s

GROUP=QA julia +1.12.7 --startup-file=no --project=. -e 'using Pkg; Pkg.test()'
QA | 21 passed / 21 total in 1m17.7s

The Runic check, typos on both changed files, and git diff --check all exited successfully with no output.

The exact Julia 1.11.9 SciMLBenchmarks page completed against this source tree and the refreshed registered stack:

timeout 14400 julia +1.11.9 --startup-file=no --threads=auto --project=. benchmark.jl benchmarks/OptimizationFrameworks/clnlbeam.jmd
exit 0 in 27:44.66, maximum RSS 4,833,580 KiB

The generated markdown had no error, exception, failure, unstable, or timeout markers. It produced a non-degenerate 576x384 plot with all six benchmark series, and every embedded objective/solution assertion passed.

Not verified

• GROUP=Everything, GPU, and Julia prerelease jobs were not run locally.
• Docs were not built because this changes neither documentation nor public API.
• Constraint Jacobian and individual constraint-Hessian batching are unchanged.

The main review judgment is reusing the existing fixed private width of 8 for Lagrangian Hessians. A row-at-a-time implementation also avoids the wide batch, but the width-8 version retains batching and reduced the focused first call by about 18 times.

Links

• Objective-Hessian batching prerequisite: Cap AutoEnzyme Hessian batches at width 8 #1331
• Source benchmark: https://github.com/SciML/SciMLBenchmarks.jl/blob/c2b5f0e46e3ba4418bb07f393949c6211f3750d8/benchmarks/OptimizationFrameworks/clnlbeam.jmd

🤖 Generated with Claude Code
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