Research map / Learning theory and algorithms / Optimal transport
Exact Optimal Accelerated Complexity for Fixed-Point Iterations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Halpern-type acceleration (OC-Halpern / OS-PPM) with optimal rate in place of Picard/PPM | nonexpansive and contractive fixed-point iterations · 2D toy example | fixed-point residual / resolvent residual | Helped |
| Restarting OS-PPM (restarted OC-Halpern) under uniform monotonicity / Hölder-type growth | PDHG for total variation CT · CT imaging | fixed-point residual | Helped |
| Restarted OC-Halpern acceleration | PDHG for earth mover's distance · Earth mover's distance | fixed-point residual | Helped |
| Restarted OC-Halpern acceleration | PG-EXTRA for decentralized compressed sensing · Decentralized compressed sensing | fixed-point residual | Helped |
| Matching lower bound: no deterministic fixed-point method can beat the OC-Halpern rate for 1/gamma-Lipschitz operators | general deterministic fixed-point iterations · theory (nonexpansive/contractive) | squared fixed-point residual rate | No clear effect |
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