ADMM and Accelerated ADMM as Continuous Dynamical Systems
Authors: Guilherme Franca, Daniel Robinson, Rene Vidal
ICML 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We numerically verify that the differential equations (10) and (21) accurately model ADMM and A-ADMM, respectively, when ρ is large as needed to derive the continuous limit. The numerical integration of the first-order system (10) is straightforward; we use a 4th order Runge-Kutta method (an explicit Euler method could also be employed). The numerical integration of (21) is more challenging due to strong oscillations. To obtain a faithful discretization of the continuous dynamical system (21), i.e., one that preserves its properties, a standard approach is to use a Hamiltonian symplectic integrator, which is designed to preserve the phase-space volume. A simple example is provided in Figure 1, which illustrate our theoretical results. |
| Researcher Affiliation | Academia | 1Mathematical Institute for Data Science, Johns Hopkins University, Baltimore MD 21218, USA. |
| Pseudocode | No | The paper presents mathematical updates for algorithms (e.g., equations 9 and 19) and numerical integration schemes (equation 59), but these are presented as mathematical expressions rather than structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement about releasing source code for the described methodology. |
| Open Datasets | No | The paper uses synthetic data described as "a random matrix with 40 zero eigenvalues and the remaining ones are uniformly distributed on [0, 10], and A is a full column random matrix with condition number 100" in Figure 1, which is not a publicly available dataset nor is any access information provided. |
| Dataset Splits | No | The paper does not specify training, validation, or test dataset splits. The numerical example in Figure 1 uses a single initial condition for a simulation rather than a dataset with splits. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run the numerical experiments. |
| Software Dependencies | No | The paper mentions numerical methods like "4th order Runge-Kutta method" and "symplectic Euler method" but does not specify any software names or version numbers (e.g., Python, PyTorch, MATLAB, specific solvers) used for implementation. |
| Experiment Setup | Yes | We choose r = 10 and ρ = 50. The initial conditions are X(0) = x0 = 5(1, 1, . . . , 1)T and X(0) = 0. |