Research map / Optimization / Nonconvex and smooth optimization
Fast Proximal Linearized Alternating Direction Method of Multiplier with Parallel Splitting
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use accelerated parameter sequences instead of the standard PALM update (theta set to 1) (ablation) | PALM · Linearly constrained convex problem, one block | convergence rate: O(1/K) -> O(1/K^2) | Helped |
| Accelerate the smooth-objective update using interpolatory sequences | PL-ADMM-PS · Linearly constrained convex problem, n>2 blocks | convergence rate: O\left(\frac{L_{\max}D_{\mathbf{x}^{*}}^2}{K} + \frac{\beta \eta_{\max}D^2_{\mathbf{x}^{*}}}{K} + \frac{D^2_{\bm{\lambda | Helped |
| Replace PL-ADMM-PS with Fast PL-ADMM-PS | PL-ADMM-PS · Extended Yale B, 5 subjects | clustering accuracy: 94.06 -> 96.88 | Helped |
| Replace PL-ADMM-PS with Fast PL-ADMM-PS | PL-ADMM-PS · Extended Yale B, 8 subjects | clustering accuracy: 85.94 -> 90.82 | Helped |
| Replace PL-ADMM-PS with Fast PL-ADMM-PS | PL-ADMM-PS · Extended Yale B, 10 subjects | clustering accuracy: 75.31 -> 75.47 | Helped |
| Linearize the augmented term to enable cheaper parallel block subproblems (ablation) | Fast PL-ADMM-PS · Linearly constrained convex problem, n>2 blocks | convergence rate: O(1/K^2) for the smooth term; O(1/K) for the remaining terms | Mixed |
| Use a fixed beta rather than an adaptive beta tied to theta (ablation) | Fast PL-ADMM-PS · Linearly constrained convex problem, n>2 blocks | convergence | Helped |
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- ADMM for Nonconvex Optimization under Minimal Continuity Assumption (ICLR 2025 · similarity 0.89)
- Faster Stochastic Alternating Direction Method of Multipliers for Nonconvex Optimization (ICML 2019 · similarity 0.89)
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