GALAHAD 2.0.0

Breaking changes

• Softplus reparameterization replaces hard-clamp positivity enforcement. Parameters in parts$positive (formerly parts$T and parts$P) are now handled internally via theta_i = softplus(z_i), guaranteeing strict positivity analytically. theta0[positive] must now be strictly > 0; v1 silently clamped zero or negative starting values, v2 raises an error.

• parts API simplified. The preferred form is now list(positive = ..., euclidean = ...). The three-way {T, P, E} form from v1 remains accepted as a backwards-compatibility alias (T and P indices both map to positive; E maps to euclidean).

New features

• Relative function-stall detection (FUNC_STALL_REL). In addition to the existing absolute stall criterion (FUNC_STALL_ABS), convergence is now also declared when |ΔV| / (|V| + ε) < tol_f_rel over five consecutive iterations. New control parameter tol_f_rel (default 1e-9).

• rho-based trust-region adaptation. The trust radius now adapts using the ratio of actual to predicted objective reduction (rho), with configurable rho_shrink (default 0.25), rho_grow (default 0.75), shrink_factor (default 0.5), and grow_factor (default 1.5). The v1 binary accept/reject heuristic is used as a fallback when rho is not finite.

• Richer per-iteration history. fit$history now contains ten columns (was eight): iter, f, g_inf, step_norm, df, eta, method, armijo_iters (new), pred_red (new), rho (new). The Lyapunov-specific columns (delta_V_rel, lyapunov_ok) from v1 are removed.

• galahad_numgrad() — exported finite-difference gradient helper for use when analytical gradients are unavailable.

• galahad_parts() — exported constructor that validates and assembles the parts argument with an optional total-parameter-count check.

• rho_accept, use_rho_accept control options enable an alternative acceptance mode based on trust-region quality ratio instead of Armijo decrease.

Changes to defaults

Removed features

• Halpern averaging removed. The per-iteration Halpern candidate alpha_k * theta0 + (1 - alpha_k) * theta_proj is no longer evaluated. This saves approximately one function evaluation per iteration; the function-stall detection provides equivalent convergence assurance on the smooth objectives for which GALAHAD is designed.

• Lyapunov violation tracking removed (lyapunov_violations, monotone_descent from diagnostics). The rho history in fit$history$rho provides equivalent information about step quality.

• make_safe_function() wrappers removed. Errors in V or gradV now surface immediately via galahad_assert_finite(). Callers are expected to supply well-defined objectives; the previous silent-fallback behaviour could mask model specification bugs.

• grad_clip_norm control option removed.

• eps_safe control option removed (no longer applicable with softplus).

Bug fixes

• Fixed a spurious st$z bare expression in the internal state-update helper that had no effect but generated lint warnings.

Citation corrections

• Polyak (1969) corrected. Version 1 incorrectly cited the paper “Minimization of unsmooth functionals”, Vol. 9(3), pp. 14–29. The correct paper implemented in GALAHAD is “The conjugate gradient method in extremal problems”, Vol. 9(4), pp. 94–112. doi:10.1016/0041-5553(69)90035-4

• Xu and An (2024) added. Citation for the regularized Barzilai-Borwein trust-region extension was absent from v1 despite the method being used. doi:10.48550/arXiv.2409.14383

• Dugas et al. (2009) added. Citation for the softplus activation function was absent from v1 despite softplus being central to the positivity geometry. Journal of Machine Learning Research, 10(42), 1239–1262. https://www.jmlr.org/papers/v10/dugas09a.html

Development note

• Development used AI coding assistance under continuous human direction; see package DESCRIPTION for full disclosure.

GALAHAD 1.0.0

• Initial CRAN release.
• Geometry-adaptive optimization with Lyapunov stability guarantees.
• Three-partition geometry: log-scaled (T), positive-only (P), Euclidean (E).
• Trust-region projection, Halpern averaging, Polyak / BB step-size control.
• Developed at MNPRO, University of Minnesota.