Crate cartan_optim 

cartan-optim

Riemannian optimization algorithms for the cartan library.

This crate implements first- and second-order optimization algorithms that operate on any manifold implementing the Manifold trait from cartan-core.

Algorithms

Algorithm	Struct/function	Trait requirements
Riemannian Gradient Descent	minimize_rgd	Manifold + Retraction
Riemannian Conjugate Gradient	minimize_rcg	+ ParallelTransport
Fréchet Mean (Karcher flow)	frechet_mean	Manifold
Riemannian Trust Region	minimize_rtr	+ Connection

Usage pattern

use nalgebra::SVector;
use cartan_core::manifold::Manifold;
use cartan_manifolds::Sphere;
use cartan_optim::{minimize_rgd, RGDConfig};

let s2 = Sphere::<3>;
let config = RGDConfig::default();
let p0 = SVector::<f64, 3>::from([0.0, 1.0, 0.0]); // start on equator

// Minimize f(p) = -p[0] (drives p toward [1, 0, 0]) on S²
let result = minimize_rgd(
    &s2,
    |p| -p[0],
    |p| s2.project_tangent(p, &SVector::from([1.0, 0.0, 0.0])),
    p0,
    &config,
);

References

• Absil, Mahony, Sepulchre. “Optimization Algorithms on Matrix Manifolds.” Princeton, 2008.
• Boumal. “An Introduction to Optimization on Smooth Manifolds.” Cambridge, 2023.

Re-exports

pub use frechet::FrechetConfig;

pub use frechet::frechet_mean;

pub use rcg::CgVariant;

pub use rcg::RCGConfig;

pub use rcg::minimize_rcg;

pub use result::OptResult;

pub use rgd::RGDConfig;

pub use rgd::minimize_rgd;

pub use rtr::RTRConfig;

pub use rtr::minimize_rtr;

Modules

frechet

Fréchet (Karcher) mean on Riemannian manifolds.

rcg

Riemannian Conjugate Gradient (Fletcher-Reeves and Polak-Ribière).

result

Optimization result type.

rgd

Riemannian Gradient Descent with Armijo line search.

rtr

Riemannian Trust Region (RTR) with Steihaug-Toint truncated CG subproblem.