Adding Heavy-Ball Momentum to Distributed Constrained Optimization for Energy Resource Management Subject to Time-Delays and Quantization
Abstract
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. 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. 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. 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. A reproducible delayed experiment reports all constants and a certificate whose guaranteed steady-state level lies below the reported initialization. A separate mixed generator-battery experiment exercises the signed update directly. Finite smooth penalties approximate, but do not generally enforce, the local box constraints exactly.
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BibTeX
@misc{doostmohammadian2026adding,
title = {{Adding Heavy-Ball Momentum to Distributed Constrained Optimization for Energy Resource Management Subject to Time-Delays and Quantization}},
author = {Mohammadreza Doostmohammadian and Sergio Pequito},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24421},
eprint = {2610.24421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24421},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Adding Heavy-Ball Momentum to Distributed Constrained Optimization for Energy Resource Management Subject to Time-Delays and Quantization
AU - Mohammadreza Doostmohammadian
AU - Sergio Pequito
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24421
UR - https://arxiv.org/abs/2610.24421
AB - 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. 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. 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. 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. A reproducible delayed experiment reports all constants and a certificate whose guaranteed steady-state level lies below the reported initialization. A separate mixed generator-battery experiment exercises the signed update directly. Finite smooth penalties approximate, but do not generally enforce, the local box constraints exactly.
ER -