Module optim 

Riemannian optimization algorithms.

Deprecated: this module has moved to descend::riemannian (enable the riemannian feature in the descend crate). The symbols here remain for backward compatibility but will be removed in a future release.

Gradient-based optimization on manifolds differs from Euclidean optimization in two ways:

1. Gradients live in tangent spaces, not in the ambient space.
2. Updates follow geodesics (via exp_map), not straight lines.

This module provides riemannian_sgd_step and riemannian_adam_step that operate on any type implementing Manifold.

References

• Bonnabel (2013), “Stochastic Gradient Descent on Riemannian Manifolds” – foundational convergence analysis for Riemannian SGD.
• Becigneul & Ganea (2019), “Riemannian Adaptive Optimization Methods” (ICLR) – extends Adam to Riemannian manifolds using parallel transport for moment vectors.

Structs

RiemannianAdamStateDeprecated

State for the Riemannian Adam optimizer.

Functions

geodesic_distanceDeprecated

Geodesic distance between two points on a manifold.

riemannian_adam_stepDeprecated

Riemannian Adam step (Becigneul & Ganea, 2019).

riemannian_sgd_stepDeprecated

Riemannian SGD step.