cartan-optim 0.1.0

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

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 cartan_manifolds::Sphere;
use cartan_optim::{minimize_rgd, RGDConfig};

let s2 = Sphere::<3>;
let config = RGDConfig::default();

// Minimize f(p) = -p[0] (find the "north pole") 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.