Geometry-Adaptive Lyapunov-Assured Hybrid Optimizer
Smooth Trust Radius Adaptation
Certified Convergence Check
Clamp Positive Parameters
Clamp Scalar to Range
Finalize Output with Lyapunov Diagnostics
GALAHAD: Geometry-Adaptive Lyapunov-Assured Hybrid Optimizer
Geometry-Aware Proximal Operator
Initialize Pre-Allocated State
Safe Function Wrapper
Normalize Geometry Partitions
Dynamic f_star Step Selection
Trust-Region Projection (Scaled M-norm)
Safe Lipschitz Update
Update Pre-Allocated State
Validate and Setup Configuration
Implements the GALAHAD algorithm (Geometry-Adaptive 'Lyapunov'-Assured Hybrid Optimizer), combining 'Riemannian' metrics, 'Lyapunov' stability checks, and trust-region methods for stable optimization of mixed-geometry parameters. Designed for biological modeling (germination, dose-response, survival) where rates, concentrations, and unconstrained variables 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>, Amari (1998) <doi:10.1162/089976698300017746>, Beck & Teboulle (2003) <doi:10.1016/S0167-6377(02)00231-6>, Nesterov (2017) <https://www.jstor.org/stable/resrep30722>, and Walne et al. (2020) <doi:10.1002/agg2.20098>.