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>.

Estimates generalized additive latent and
    mixed models using maximum marginal likelihood, 
    as defined in Sorensen et al. (2023) 
    <doi:10.1007/s11336-023-09910-z>, which is an extension of Rabe-Hesketh and
    Skrondal (2004)'s unifying framework for multilevel latent variable 
    modeling <doi:10.1007/BF02295939>. Efficient computation is done using sparse 
    matrix methods, Laplace approximation, and automatic differentiation. The 
    framework includes generalized multilevel models with heteroscedastic 
    residuals, mixed response types, factor loadings, smoothing splines, 
    crossed random effects, and combinations thereof. Syntax for model 
    formulation is close to 'lme4' (Bates et al. (2015) 
    <doi:10.18637/jss.v067.i01>) and 'PLmixed' (Rockwood and Jeon (2019) 
    <doi:10.1080/00273171.2018.1516541>).