scipy.optimize: fix signed bracket width in line search zoom

[VaggelisGian]

Description

jax.scipy.optimize.minimize(method="BFGS") reports a line-search failure (status 3) on the classical 2D Rosenbrock function from the standard start points, in both float32 and float64, where scipy.optimize.minimize converges:

JAX_ENABLE_X64=1, x0=[0,0]:     success=False status=3 nit=1 fun=0.77657
JAX_ENABLE_X64=1, x0=[-1.2,1]:  success=False status=3 nit=8 fun=1.74729
float32,       x0=[-1.2,1]:     success=False status=3 nit=8 fun=1.74729

Root cause is in the zoom stage of the Wolfe line search (jax/_src/scipy/optimize/line_search.py). The failure guard compared a signed bracket width dalpha <= threshold. zoom2 is always entered with a_lo > a_hi whenever the outer loop doubled alpha, and zoom1 legitimately inverts its bracket after swaps, so on those iterations a negative width compared against a positive threshold set the sticky failed flag even while the bracket still contained steps satisfying the strong Wolfe conditions - scipy's line_search_wolfe2 returns the identical step for the same inputs.

Second, the absolute thresholds (1e-5 narrow dtypes, 1e-10 otherwise) were neither scale nor dtype aware and rejected legitimate deep bisection (widths near 1e-12 on steep quadratics).

The guard now compares abs(dalpha) against eps(dtype) * max(|a_lo|, |a_hi|), the width below which bisection cannot produce a distinct midpoint, and the zoom iteration cap moves from 30 to 60 so pure-bisection searches over wide dynamic ranges can finish.

Deliberately unchanged: the Wolfe condition definitions, the outer loop, and the float32 alpha floor in line_search. One interaction worth noting: the newly reachable deep zooms can end on an alpha below that pre-existing floor (|alpha_k| < 1e-8 is floored to 1e-8 for narrow dtypes), so on problems with extreme curvature in float32 the L-BFGS path can report convergence at a step whose stored alpha was floored. That is pre-existing floor behavior on a previously unreachable path and is left to a separate change.

AI assistance disclosure: this fix was developed with AI coding assistance under my direction; I verified the root cause analysis, ran all tests shown below, and take responsibility for the change.

Test Plan

New tests use the classical Rosenbrock valley (the file's existing helper squares plain differences and never forms it):

python -m pytest tests/scipy_optimize_test.py -k "curved_valley or steep_quadratic" -q
  default flags: 2 failed before the fix, 2 passed + 3 skipped after.
JAX_ENABLE_X64=1 python -m pytest tests/scipy_optimize_test.py -k "curved_valley or steep_quadratic" -q
  x64: 5 failed before the fix, 5 passed after.
python -m pytest tests/scipy_optimize_test.py -q -n auto
  default flags: 15 passed, 4 skipped.
JAX_ENABLE_X64=1 python -m pytest tests/scipy_optimize_test.py -q -n auto
  x64: 19 passed.

All previously-converging cases were checked for drift before/after: standard objectives converge to bit-identical results or shift by at most one iteration.

References

• Wrong definition of interval length in zoom linesearch #16236 is the canonical issue for the signed-width defect: it names dalpha = a_hi - a_lo < 0 at exactly these lines and prescribes jnp.abs(dalpha); this PR implements that prescription plus the dtype/scale-aware threshold the absolute-constant version still needed. BFGS line search behavior in steep loss landscapes departs from SciPy Minimize #4594 reports the same status=3 symptom from the user side. The a_rec slot correction in 88d98bd fixed an adjacent zoom-state bug only; the signed-threshold guard remained untouched on main.