Adding Heavy-Ball Momentum to Distributed Constrained Optimization for Energy Resource Management Subject to Time-Delays and Quantization

Key points

• The method preserves the aggregate supply-demand equality at every iteration.1
• For a static connected undirected graph and bounded delays, a Lyapunov-Krasovskii analysis establishes practical stability by isolating the discontinuous quantization error as an additive disturbance and closing a computable invariant-sublevel argument.1
• The resulting ergodic residual bound is quadratic in the quantization resolution, and exact convergence to the smooth penalized equality-constrained optimizer is recovered in the unquantized case.1
• For delay-free unquantized quadratic costs, an exact modal analysis identifies the heavy-ball stability region and optimal parameters, with the predicted rate validated on a fixed sparse network.1

Sources (1)

• [1]Adding Heavy-Ball Momentum to Distributed Constrained Optimization for Energy Resource Management Subject to Time-Delays and Quantization
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 17, 03:37 AM

  This paper studies a hybrid discrete-time signed gradient-consensus method with heavy-ball momentum, paired communication delays, and fixed logarithmic quantization.

  The method preserves the aggregate supply-demand equality at every iteration.

Extractive summary: sentences quoted from the sources.