[FFroehlich]

Fixes #78

Problem

update_tr_radius only increases the radius when the step is at least 0.9 * delta long. A step that was stepped back to stay within the bounds (step.alpha < 1) is shorter than that because of the bounds, not because of the trust region. So the radius never grew for such steps, even at tr_ratio ≈ 1. With reflect_single and several active bounds, every iteration's best step is a single reflection that the next bound cuts short. On the 4-D reproducer from the issue, the radius stays at 2 and the run crawls to MAXITER (1000 steps, median alpha 0.13).

Change

fides/minimize.py, one line in update_tr_radius. Whether the trust-region constraint was active is now decided on the proposal before step back, norm(step.og_ss + step.ss0), instead of on the step that is taken:

• Steps that were not stepped back (alpha == 1, so og_ss == ss): unchanged.
• Stepped-back steps whose proposal reached the trust-region boundary count as boundary steps. A good ratio grows the radius, as it would have without the bound. This is the reflect_single case.
• Stepped-back steps whose proposal was interior to the trust region (e.g. a Newton step that hits a bound) still do not grow the radius. A larger radius would not change that proposal.

Why not option 1 from the issue (alpha < 1 ⇒ boundary step)

Option 1 fixes the 2D reproducer but makes the radius grow without bound whenever bound-limited steps keep a good ratio. With scg + reflect_single on the issue's reproducer, the radius doubles every iteration while the step stays about 1 long. It reaches 1e301 at iteration 1000 and inf at about 1024, and the run still hits MAXITER. In the fuzz run below (first 33 problems), option 1 also changed the exit of the other strategies, from FTOL/GTOL to DELTA_TOO_SMALL, with many more rejected steps:

33 problems × 42 configs	main DELTA_TOO_SMALL	option 1	this PR	main rejected steps	option 1	this PR
truncate	7	28	7	663	1017	663
mixed	7	13	7	670	769	670
refine	0	17	0	312	565	297
reflect_single	4	14	4	597	790	604

This partial run still used a wall-clock time limit. The refine row excludes the runs that hit it: 4 on main, 13 with option 1, 11 with this PR. The full comparison below re-runs those with a CPU-time limit.

Fuzz: main vs this PR

300 random problems (seeds 100–399 of the #75 fuzz set: bounded quadratics and Rosenbrock, n = 1–12, five box types, four start types) × 42 configurations (2D/full/scg × all step-back strategies × exact/BFGS/SR1; scg has no refine), maxiter = 500. That makes 12,600 runs per side. Runs that hit the time limit on either side were re-run on both sides with a 60 s CPU-time limit (70 per side, none timed out). "Optimum" means f - fref <= 1e-6 + 1e-4 |fref|, against a scipy BVLS / L-BFGS-B reference.

strategy	runs	MAXITER main → PR	at optimum main → PR	fixed	broken	iterations (sum) main → PR	rejected steps main → PR
reflect_single	2700	98 → 56	2428 → 2461	33	0	146,176 → 120,652	10,895 → 11,038
reflect	2700	49 → 47	2465 → 2468	3	0	111,461 → 110,191	11,107 → 11,181
truncate	2700	47 → 48	2470 → 2470	0	0	108,145 → 108,382	11,361 → 11,393
mixed	2700	42 → 42	2471 → 2471	0	0	107,052 → 107,036	11,503 → 11,498
refine	1800	46 → 41	1673 → 1676	4	1	76,124 → 74,342	7,086 → 7,086

By solver, MAXITER for reflect_single goes 18 → 7 (2D), 29 → 29 (full) and 51 → 20 (scg). For reflect on scg it goes 16 → 13. No exceptions, NaN returns or bound violations on either side.

The one broken run (seed 172, Rosenbrock, 2D/refine/BFGS, FTOL → MAXITER) and the single-run changes for truncate/reflect (seeds 229 and 346, nonconvex Rosenbrock with quasi-Newton updates) come from trajectory divergence. In each, the new rule changed the radius decision at 1–4 iterations and the rest of the path differs. Neither side reached the optimum in the truncate/reflect cases.

Not fixed here

scg + reflect_single on the issue's reproducer still stalls. Steihaug CG stops after one iteration there (residual tolerance 0.5 |g|, #77), so the CG step is the gradient step. That step is dominated by the two variables on their bounds and is cut at alpha ~ 1e-3, and its single reflection hits the other bound. The step length does not depend on the radius, so no radius rule helps. The new regression test therefore covers 2D/full.

Tests

• test_several_active_bounds: the issue's 4-D reproducer for 2D/full × all step-back strategies, maxiter = 100. It asserts no MAXITER and the optimum in f and x. On main, 2D-reflect_single and 2D-refine fail (MAXITER far from the optimum); here they converge in 12 and 15 iterations. The test does not require a positive exit flag because full/refine stops with DELTA_TOO_SMALL at the optimum, on main as well. The predicted decrease there is below the resolution of f, which is unrelated to this change.
• pytest tests: 1229 passed, 3 skipped (after merging current main).

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.03%. Comparing base (586389f) to head (91d78d8).

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #90   +/-   ##
=======================================
  Coverage   97.03%   97.03%           
=======================================
  Files          10       10           
  Lines        1179     1179           
=======================================
  Hits         1144     1144           
  Misses         35       35           

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