Research map / Optimization / Nonconvex and smooth optimization
Accelerated Gradient Methods for Geodesically Convex Optimization: Tractable Algorithms and Convergence Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Riemannian NAG-style momentum (RNAG-C) instead of Riemannian gradient descent | Rayleigh quotient maximization on sphere · Rayleigh quotient maximization (d=1000) | objective gap convergence | Helped |
| Use RNAG-SC instead of Riemannian gradient descent on strongly convex Karcher mean | Karcher mean of SPD matrices · Karcher mean SPD (d=100, n=50) | objective gap convergence | Helped |
| Use RNAG-C on well-conditioned g-strongly convex Karcher mean problem | Karcher mean of SPD matrices · Karcher mean SPD (d=100, n=50) | objective gap convergence | No clear effect |
| Set xi = zeta + 3(zeta - delta) in RNAG-C (friction/metric-distortion correction) | RNAG-C · theory: g-convex | iteration complexity O(xi sqrt(L/eps)) | No clear effect |
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