Fix gradient norm scaling in pounders convergence checks

[timmens]

Fixes #657.

Problem

POUNDERS fits its residual model in coordinates scaled by the trust-region radius, (x - center) / delta. The model's linear_terms therefore already equal delta * gradient. The convergence checks multiplied this by delta again, so convergence_gtol_abs, convergence_gtol_rel and convergence_gtol_scaled compared delta**2 * ||gradient|| against the tolerances.

Once the trust region shrank, runs reported "Norm of the gradient relative to the criterion value is less than relative_gradient_tolerance" at points far from the minimum. From the start vector [1e-6, 1e-6, 1e-6] the iteration path is chaotic: a relative perturbation of 1e-15 changes where it ends. Tiny floating-point differences between platforms then decided whether the run hit the minimum. That explains the scattered results in #657. None of the reported Linux results were minima (criterion 2455 to 3922, optimum 2384.48). In one traced run the true gradient was about 5e5 while the tested norm was 7e-4.

Fix

Use ||linear_terms|| / delta, the gradient in the original coordinates. This matches Stefan Wild's reference implementation (IBCDFO formquad.m returns G / delta, which pounders.m compares against g_tol), and the docs, which describe the criterion as the norm of the gradient. The double scaling was copied from PETSc TAO's pounders.c (gnorm *= mfqP->delta) in the original port.

Tests that previously failed now run

Test	Before	After
test_bntr (all 5 cases, including start_vec3-cg, which failed in #657)	Skipped on Linux (all Python versions) and Windows. Ran on macOS only.	Runs on Linux, Windows and macOS. No skips left.
test_bntr assertions	Parameters only (decimal=3)	Parameters, plus final criterion value 2384.477 (abs 1e-2)
test_bntr_no_false_convergence_under_start_value_jitter (new, slow)	n/a. Fails on main: 4 of 10 jittered runs stop away from the minimum.	Passes: 10 of 10 reach the minimum. Runs on Linux CI (tests-with-cov).

Locally (macOS): pounders tests 100 passed, 1 skipped, 1 xfailed. tests/optimagic/optimizers, test_many_algorithms and test_estimate_msm: 647 passed, 12 skipped, 1 xfailed. This PR's CI is the first run of test_bntr on Linux and Windows since the skips were added.

Behavior change

Stopping changes for all POUNDERS users. Robustness and cost with 1e-15 start value jitter, 20 runs per case:

	Runs at the minimum	Median iterations, start [0.15, 0.008, 0.01]	Median iterations, start [1e-6]*3
Before	17 to 19 of 20	22	70
After	20 of 20	35	96

With the correct gradient norm, the default gradient tolerances (1e-8) rarely trigger. Most runs now stop because the model was identical in successive iterations. Whether the default tolerances should change is a separate question.

Suggested CHANGES.md entry:

Fix the gradient norm in the pounders convergence checks, which was scaled by the squared trust-region radius ({gh}657). The gtol criteria now use the model gradient in the original coordinates. Stopping may take more iterations (about 50% more with default tolerances in our tests), and reports of convergence at non-minima are much rarer.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

Files with missing lines	Coverage Δ
src/optimagic/optimizers/pounders.py	92.46% <100.00%> (-0.11%)	⬇️

... and 4 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[timmens]

CI confirms that the previously skipped test_bntr cases now run and pass on Linux and Windows. All checks are green.

Before (latest main run, run 30351008031), s = skipped:

ubuntu-latest py313:  tests/optimagic/optimizers/test_pounders_integration.py sssss.
windows-latest py313: tests\optimagic\optimizers\test_pounders_integration.py sssss.

After (this PR, run 36701300636):

ubuntu-latest py313:  tests/optimagic/optimizers/test_pounders_integration.py .......
windows-latest py313: tests\optimagic\optimizers\test_pounders_integration.py ......

The five sssss are the test_bntr cases, including start_vec3-cg from #657. On Linux, the seventh test is the new slow regression test test_bntr_no_false_convergence_under_start_value_jitter. Windows runs tests-fast, which deselects slow tests. The same holds for the py312 and py314 jobs.