scipy.optimize: report ftol termination in L-BFGS as converged

[VaggelisGian]

Description

In jax.scipy.optimize.minimize(method="l-bfgs-experimental-do-not-rely-on-this"), an iteration whose function decrease satisfied (f_k - f_{k+1}) < ftol was recorded as status 4 ("insufficient progress") while the converged mask tested only the gradient norm. Such runs ended with success=False even though they met the requested tolerance. SciPy's L-BFGS-B treats the same condition as convergence.

The ftol condition now feeds converged, so an ftol-stopped run reports converged=True, status 0, success=True, provided the line search at that iteration succeeded. If the line search failed at that iteration, the run still ends as a failure exactly as before (a failed search returns a finite objective decrease that would otherwise masquerade as ftol convergence). Status value 4 no longer occurs; termination points are unchanged for every input - such iterations previously stopped the loop via failed and now stop it via converged.

Deliberate scope limit: the ftol criterion stays an absolute decrease, unlike SciPy's relative reduction over max{|f_k|, |f_{k+1}|, 1}. The absolute form is what the docstring has always documented, switching would move termination points for existing inputs, and JAX already disclaims result parity with SciPy for this method.

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

python -m pytest tests/scipy_optimize_test.py -k "ftol_termination or default_termination or gtol_convergence or ftol_not_reported or ftol_takes_precedence" -q
  default flags: green after the fix; test_ftol_not_reported_when_line_search_fails fails against the unfixed tree with
  AssertionError: Array(True, dtype=bool) is not false
python -m pytest tests/scipy_optimize_test.py -k "minimize or bfgs or lbfgs" -q
  default flags: 18 passed, 1 skipped.
JAX_ENABLE_X64=1 python -m pytest tests/scipy_optimize_test.py -k "minimize or bfgs or lbfgs" -q
  x64: 19 passed.
python -m pytest tests/scipy_optimize_test.py -q   (full file)
  default flags: 18 passed, 1 skipped; x64: 19 passed.

Byte-level probes confirm identical nit/nfev/x/fun before and after the change for gtol-only and default runs; only the success/status reporting of ftol stops flips.

References

• L-BFGS fails when ftol is met #15486 reported exactly this ("L-BFGS fails when ftol is met") and closed without a fix. This PR is the minimal reporting fix for the method as shipped; no parity beyond clean stops is claimed, and the absolute-ftol semantics are unchanged. I am aware of the sentiment in that thread favoring directing users to jaxopt - until any deprecation actually lands, users of this method still hit the failure reporting, and this change alters nothing except that reporting.