Use Anderson acceleration for the TPI outer loop: 2x faster transition paths

[vahid-ahmadi]

Why

OG-Core ships an Anderson accelerator for the TPI outer loop, but TPI_outer_method defaults to "picard" — damped functional iteration at nu=0.4. OG-UK has never used it. It is available under the current ogcore<0.18 pin (shipped in 0.17.0), so this needs no version change and no migration.

What changes after merging

Single-sector transition paths take half as long: 16 outer iterations → 8, ~95s → ~47s at production shape. Same equilibrium. Multi-sector runs are unchanged.

This is the only PR in this set that changes numerical behaviour, so the evidence is below in full.

Benchmark

Run through _build_specs with live calibration at OG-UK's own defaults — S=80, J=7, T=60, M=1, pooled GS, ogcore 0.17.0. SS solved once per scenario and reused by both arms; sequential runs, identical single-worker client; only TPI_outer_method differs.

arm	method	iters	final TPIdist	wall clock
baseline	picard	16	7.291e-05	94.9 s
baseline	anderson	8	3.979e-05	47.7 s
reform (CIT 27%→32%)	picard	16	7.456e-05	95.3 s
reform	anderson	8	4.709e-05	46.9 s

Same equilibrium — max relative difference between the two paths, all inside mindist_TPI = 1e-4:

	Y	K	L	r	w	C
baseline	7.7e-06	2.1e-06	6.9e-06	3.1e-05	8.5e-06	1.5e-05
reform	8.6e-06	3.9e-06	7.2e-06	3.7e-05	1.0e-05	1.3e-05

Diagnostics — no stall, no divergence, nothing non-finite. Each anderson run logged exactly one accel step worsened; trust radius -> 0.5: the trust-region guard firing and recovering, after which the residual falls monotonically (0.106, 0.188, 0.082, 0.031, 9.5e-3, 1.5e-3, 3.7e-4, 4.0e-5). Picard is monotone but slow after iteration 4.

A smaller run (S=40, J=2, T=120, OG-Core test params) gave the same 1.9x and was insensitive to TPI_anderson_m ∈ {2,5,10} and TPI_trust_radius ∈ {0,1,2}, defaults best of the set.

Change

tpi_outer_method(multi_sector) returns "anderson" for single-sector and "picard" otherwise; _build_specs uses it. The trust-region guard is left at its default — it demonstrably does work here, so the unguarded variant is not used.

Multi-sector deliberately keeps Picard: M=8 uses hybr with relaxed SS tolerances and has no evidence either way. Obvious follow-up if someone wants to benchmark it.

Extracted as a standalone function so it can be tested without a live calibration — _build_specs itself calibrates, which makes it unusable in a fast test.

Evidence

4 tests, 1.25s: single-sector selects anderson, multi-sector stays on picard, both values still accepted by OG-Core's update_specifications (guards against an upstream rename), trust radius positive by default.

Full suite 13 passed, 3 skipped. ruff clean.

Incidental

Every arm reported max_RC_error ≈ 0.158 (baseline) / 0.160 (reform), method-independent to six significant figures. That is the RC_TPI = 0.2 waiver discussed in #72 and fixed by #75 — independent confirmation at production shape, unrelated to this change.

Addresses the performance half of #76.