Samplinglib · research resources
Geometry and transport
Keep the ambient space, metric and geometric structure visible. Read manifold optimization and statistical transport together where useful, without identifying their different notions of gradient or curvature.
Choose a reading route
Riemannian Optimization
Boumal's manifold geometry and optimization route
Statistical Optimal Transport
Chewi, Niles-Weed and Rigollet; couplings, duality and statistics
Keep the argument inspectable
Choose the space
Specify manifold, tangent space, Riemannian metric, retraction or geodesic. For transport, state measures, moments, couplings and the transport cost.
Identify the adapter
Ask which Euclidean ingredient survives and which metric-dependent inequality must be proved anew. A similar proof diagram is not a theorem that transports between spaces.
Expose the boundary
Distinguish geodesic convexity, displacement convexity and analytic curvature assumptions. Check completeness, cut loci, optimizer existence and moment hypotheses where the argument uses them.
Title-based discovery links below suggest reading, not source equivalence or a certified Euclidean-to-Riemannian/Wasserstein transport.
Related research to inspect
Title-based suggestions from the pinned Forum bibliography. Placement is a discovery aid only; no claim is made that these papers were read, formalized or assigned to a source chapter.
- Sliced Wasserstein Barycenters: The Analysis Approach within the Barycentric Coding Model in the Wasserstein Space external reference
- Annealed Sinkhorn with Momentum: Certified Unregularized Optimal Transport in Linear Memory external reference
- From Manifold Identification to Newton Acceleration on Intersections: Sparse Stiefel Optimization external reference
- Sharp \(O(1/k)\) convergence rate for the Sinkhorn algorithm via a local analysis external reference
- Almost-sharp \(O(k^{-1} \log k)\) convergence rate for the Sinkhorn algorithm in the asymptotically scalable case external reference
- All roads lead to Rome: Path-following Augmented Lagrangian Methods via Bregman Proximal Regularization external reference
- Robust Sublinear Convergence Rates for Iterative Bregman Projections external reference
- Trajectory-Wise Certification for Vector-Field Mirror Descent with Deterministic Finite Differences external reference
- Tight lower bounds for Lipschitz geodesically convex optimization on hyperbolic space external reference
- Does Policy Mirror Descent Converge in Policy with Non-Decomposable Mirror Maps? A Counterexample external reference
- The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity external reference
- Curvature-Dependent Lower Bounds for Frank-Wolfe external reference