Research map / Optimization / Nonconvex and smooth optimization
Conformal Symplectic and Relativistic Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RGD instead of CM and NAG | Optimization problems with large gradients or fast-growing tails · Beale function | convergence | Helped |
| Use RGD instead of CM and NAG | Optimization problems with large gradients or fast-growing tails · Zakharov function | convergence | Helped |
| Use RGD instead of CM and NAG | Optimization problems with large gradients or fast-growing tails · Three-hump camel back function | convergence | Helped |
| Set relativistic normalization strength δ > 0 (ablation) | RGD · Beale function | convergence | Helped |
| Set relativistic normalization strength δ > 0 (ablation) | RGD · Schwefel function | convergence | Helped |
| Set relativistic normalization strength δ > 0 (ablation) | RGD · Zakharov function | convergence | Helped |
| Choose α near 1 to retain conformal symplecticity (ablation) | RGD · Correlated quadratic | convergence | Helped |
| Choose α = 1 instead of α = 0 (ablation) | RGD · Quadratic stability analysis | stability | Helped |
| Use a second-order conformal symplectic discretization rather than first-order CM (ablation) | RGD · Quadratic stability analysis | stability | Helped |
| Introduce Hessian-dependent spurious damping | NAG relative to CM · Quadratic stability analysis | stability | Hurt |
| Introduce Hessian-dependent spurious damping | NAG relative to CM · Quadratic stability analysis | convergence rate | Helped |
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