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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