Research map / Optimization / Nonconvex and smooth optimization
Unifying Nesterov's Accelerated Gradient Methods for Convex and Strongly Convex Objective Functions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Unified AGM (adaptive momentum unifying AGM-C and AGM-SC) instead of AGM-C or AGM-SC alone | Unified AGM · ℓ2-regularized logistic regression, µ from 10^-1 to 10^-5 | f(x_k)-f(x*) | No clear effect |
| Unified ATM (higher-order unified method) instead of ATM-C or ATM-SC alone | Unified ATM · Cubic-regularized linear regression, µ from 3·10^-3 to 3·10^-9 | f(x_k)-f(x*) | No clear effect |
| AGM-SC instead of AGM-C when µ is large vs small | AGM-SC · ℓ2-regularized logistic regression | f(x_k)-f(x*) | Mixed |
| Adding the unified time-varying momentum (unified AGM ODE/algorithm) with an ill-conditioned strongly convex objective | Unified AGM vs AGM-C · Theory: convergence rate bound | convergence rate bound | Helped |
| Unified AGM-G ODE for minimizing gradient norm of strongly convex functions vs OGM-G ODE | Gradient-norm ODE · Theory: gradient norm convergence | convergence rate bound | Helped |
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