Research map / Optimization / Nonconvex and smooth optimization
Lyapunov Functions for First-Order Methods: Tight Automated Convergence Guarantees
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Restrict Lyapunov function by fixing λij = 0 (drop interpolation multipliers for the positive-definiteness condition) (ablation) | quadratic Lyapunov search (ρ-SDP) · smooth strongly convex, methods GM/HBM/FGM/TMM | best achievable worst-case rate ρ | Hurt |
| Replace IQC-style constraints with full interpolation conditions (including function-value constraints) in the SDP | quadratic Lyapunov search (ρ-SDP) · smooth strongly convex minimization | convergence rate ρ | Helped |
| Use exact line search in gradient method instead of fixed step 1/L | Gradient Method · smooth strongly convex, subspace search | worst-case rate ρ | Helped |
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