GALAHAD

Geometry-Adaptive Lyapunov-Assured Hybrid Optimizer with Softplus Reparameterization and Trust-Region Control

Implements the GALAHAD algorithm (Geometry-Adaptive Lyapunov-Assured Hybrid Optimizer), updated in version 2 to replace the hard-clamp positivity constraint of v1 with a numerically smooth softplus reparameterization, add rho-based trust-region adaptation (actual vs. predicted objective reduction), extend convergence detection to include both absolute and relative function-stall criteria, and enrich the per-iteration history with Armijo backtrack counts and trust-region quality ratios. Parameters constrained to be positive (rates, concentrations, scale parameters) are handled in a transformed z-space via the softplus map so that gradients remain well-defined at the constraint boundary. A two-partition API (positive / euclidean) replaces the three-way T/P/E partition of v1; the legacy form is still accepted for backwards compatibility. Designed for biological modeling problems (germination, dose-response, prion RT-QuIC, survival) where rates, concentrations, and unconstrained coefficients coexist. Developed at the Minnesota Center for Prion Research and Outreach (MNPRO), University of Minnesota. Based on Conn et al. (2000) <doi:10.1137/1.9780898719857>, Barzilai and Borwein (1988) <doi:10.1093/imanum/8.1.141>, Xu and An (2024) <doi:10.48550/arXiv.2409.14383>, Polyak (1969) <doi:10.1016/0041-5553(69)90035-4>, Nocedal and Wright (2006, ISBN:978-0-387-30303-1), and Dugas et al. (2009) <https://www.jmlr.org/papers/v10/dugas09a.html>.

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