Add a general-objective trust-region optimizer (EFIM / JᵀJ Hessian) — the general-NLL × trust-region cell currently falls back to lbfgs quasi-Newton

[wshlavacek]

The gap

PyBNF's gradient-based local optimizers currently cover three of the four cells of the natural (objective × curvature-model) matrix:

	least-squares (SOS / chi_sq)	general NLL (estimated σ, Laplace/count, constrained)
trust-region, EFIM JᵀJ Hessian	trf ✅	— missing —
quasi-Newton	(trf preferred)	lbfgs ✅

The moment an objective stops being a pure sum-of-squares — an estimated noise scale, a Laplace/count likelihood, or a constrained fit — the gradient path drops from trf's trust-region-with-JᵀJ step down to lbfgs quasi-Newton. On the ill-conditioned NLL landscapes typical of these problems that's a real downgrade: an empirical-Fisher (JᵀJ) trust-region step is far better conditioned and converges faster and more reliably than a limited-memory BFGS Hessian built from gradient differences. We already get that benefit for least-squares via trf; we lose it exactly where the objective gets harder.

What's requested

A general-objective trust-region optimizer whose Hessian is the empirical Fisher information (JᵀJ, Gauss–Newton) — i.e. trf's step quality, extended to any NLL objective lbfgs currently handles. Registered as a fit type, running under the existing multi-start gradient orchestrator (gradient_base) like trf/lbfgs.

Why it's tractable — most of the machinery already exists

• trf already assembles the residual Jacobian and forms JᵀJ via the Coleman–Li affine scaling; generalizing the EFIM-trust-region step to an arbitrary NLL is an extension of that machinery, not a green-field build.
• No new backend capability is required. The EFIM Hessian is a first-order object — Σ (∂Y/∂θ)ᵀ Σ⁻¹ (∂Y/∂θ) — built entirely from the forward output-sensitivity tensor trf and lbfgs already consume via the [Epic] Gradient plumbing: objective gradients & residual Jacobians from the BNGsim output-sensitivity tensor #385 gradient plumbing (bngsim even packages this exact object as its FIM). The general-objective terms (estimated-σ block, non-Gaussian per-observation factors, constraints) are analytic and assemble on the PyBNF side from those same sensitivities. No second-order sensitivities needed — avoiding them is the point of the EFIM approximation.

Design decision

Native EFIM-TR vs. an optional pip backend. Recommend native: a picklable, explicit step machine consistent with trf/powell (scipy stays a test-oracle only, never a blocking in-loop driver), so backup/resume and the distributed propose/score loop keep working and a fit can run N starts concurrently.

Scope / acceptance

• New fit type on the GradientOptimizer base; no run() override (ADR-0007).
• Handles the objectives trf refuses: estimated noise scale, Laplace/count likelihoods, BPSL-constrained fits.
• Step math validated against a scipy/oracle reference in tests, as with trf.