[aarontrowbridge]

Closes #163.

What

Under MadNLP's hessian_approximation = "compact_lbfgs", the L-BFGS update asks for $J^\top l$ via MOI.eval_constraint_jacobian_transpose_product on every iteration, and the evaluator answered each request by re-evaluating the full constraint Jacobian. On spline-integrator problems that is ~45% of wall time, booked by MadNLP as "solver (w/o init./fun./lin. alg.)" rather than as function evaluations (profiled: 328 s of 714 s over 4 iterations on a 30-knot ket spline problem; 22,046 s of a 44,335 s production solve).

The evaluator now keeps a two-slot FIFO cache of (exact copy of the packed iterate, Jacobian values), filled by eval_constraint_jacobian and by any product that had to recompute. J·w / Jᵀw at a bit-identical iterate (elementwise isequal, no tolerance) reuse the stored values with zero allocation.

Why two slots: MadNLP 0.9 requests $J^\top l$ at the previous iterate (qn.last_x) right after evaluating $J$ at the current one. A single same-iterate slot gets 1 hit in 15 iterations; LRU gets 2; FIFO with two slots gets 15/15.

Correctness

Returned values are unchanged. A seeded 15-iteration compact_lbfgs solve on the standard test problem has a bit-identical per-iteration trace (k, obj, inf_pr, inf_du), objective, iteration count, and final iterate with the cache on vs off, with hits ≥ iterations − 1. evaluator._jacobian_cache_enabled = false restores the old path (used as the test baseline).

Tests

7 new testitems (hit after eval for both products, zero-allocation hit path, recompute + refresh at a different iterate including a one-ulp change, in-place mutation of the caller's buffer is not a stale hit, cold cache, L-BFGS access pattern, the bit-identical MadNLP solve). Targeted local run: 48/48 pass. Full suite: this PR's CI.

Found along the way (not fixed here)

MadNLPMOI's eval_constraint_jacobian_transpose_product(::Optimizer, …) writes the qp_data (linear-constraint) contribution into Jtv before calling the NLP evaluator, and our evaluator starts with fill!(y, 0), erasing it. For problems with affine MOI constraints the L-BFGS $y_k$ may be missing $-A_\text{lin}^\top l$. Pre-existing; will file separately once confirmed.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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[aarontrowbridge]

Production-problem A/B (bosonic GKP |0_L⟩ prep, 30-knot ket spline, state dim 200, 6,083 variables; Modal 8 cores each, same image except DirectTrajOpt): resume from the same checkpoint, 4 MadNLP compact_lbfgs iterations.

	v0.11.0	this PR
MadNLP iteration table (k, obj, inf_pr, inf_du, …)	—	identical, all 5 rows
final F (independent rollout, 1e-12)	0.987249158	0.987249158
NLP function evals	388.8 s	264.6 s
solver (w/o init./fun./lin. alg.)	333.2 s	66.8 s
total	723.9 s	332.9 s (2.17×)