Research map / Optimization / Nonconvex and smooth optimization
Continuous-Time Analysis of Accelerated Gradient Methods via Conservation Laws in Dilated Coordinate Systems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Analyze AGM ODE (r>3) via conservation law in dilated coordinates instead of prior Lyapunov function | AGM ODE r>3 · continuous-time convex minimization | f(X)-f* bound constant: (r-1)^2/2 improved to (r-1) | Helped |
| Semi-second-order symplectic Euler discretization in dilated coordinates of AGM ODE | discretized AGM · smooth convex minimization, discrete k | O(1/k^2) rate constant | Helped |
| Concatenate AGM ODE with OGM-G ODE to obtain gradient-norm rate | OGM-G ODE · smooth convex minimization, gradient norm | ||grad f||^2 rate O(1/T^4) | Helped |
| Generalize OGM-G ODE to r<-3 with dilated coordinates | OGM-G ODE · smooth convex minimization, gradient norm | ||grad f(X(T))||^2 bound constant | No clear effect |
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