Research map / Optimization / Nonconvex and smooth optimization
Accelerated First-order Methods for Geodesically Convex Optimization on Riemannian Manifolds
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace linear extrapolation with nonlinear Riemannian operator (accelerated method) for strongly G-convex objectives | Riemannian gradient descent · geodesically strongly convex smooth problems | convergence rate | Helped |
| Accelerated method for general G-convex objectives | Riemannian gradient descent · geodesically general convex smooth problems | convergence rate | Helped |
| Accelerated method instead of RGD on Karcher mean problems | Karcher mean SPD matrix problem · d=100 and d=200, N=100 synthetic SPD | distance to optimum vs. running time | Helped |
| Accelerated method compared with LRBFGS on Karcher mean problems | Karcher mean SPD matrix problem · d=100 and d=200, N=100 synthetic SPD | distance to optimum vs. iterations | Mixed |
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