cartan-optim 0.5.0

Riemannian optimization algorithms for cartan: Riemannian gradient descent, conjugate gradient, trust region
Documentation

cartan-optim

Riemannian optimization algorithms for cartan.

crates.io docs.rs

Part of the cartan workspace.

Overview

cartan-optim implements first- and second-order optimization algorithms that operate on any manifold implementing traits from cartan-core. Each algorithm requires progressively richer geometry:

Algorithm Function Trait requirements
Riemannian Gradient Descent minimize_rgd Manifold + Retraction
Riemannian Conjugate Gradient minimize_rcg + ParallelTransport
Riemannian Trust Region minimize_rtr + Connection
Frechet Mean (Karcher flow) frechet_mean Manifold

All solvers return an OptResult containing the final point, objective value, gradient norm, and iteration count.

Example

use nalgebra::SVector;
use cartan_core::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]);

// Minimize f(p) = -p[0] on S^2, driving p toward [1, 0, 0].
let result = minimize_rgd(
    &s2,
    |p| -p[0],
    |p| s2.project_tangent(p, &SVector::from([1.0, 0.0, 0.0])),
    p0,
    &config,
);

License

MIT