Distributed Nonconvex Optimization with Exponential Convergence Rate via Hybrid Systems Methods
Year: 2026
Type: article
Abstract: We present a hybrid systems framework for distributed multi-agent optimization in which agents execute computations in continuous time and communicate in discrete time. The optimization algorithm is analogous to a continuous-time form of parallelized coordinate descent. Agents implement an update-and-hold strategy in which gradients are computed at communication times and held constant during flows between communications. The completeness of solutions under these hybrid dynamics is established. Then, we prove that this system is globally exponentially stable to a minimizer of a possibly nonconvex, smooth objective function that satisfies the Polyak-Łojasiewicz (PL) condition. Simulation results are presented for three different applications and illustrate the convergence rates and the impact of initial conditions upon convergence.
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Awards: G1257962346, G1523888516, G2186954028, Collaborative Research: CPS: Frontier: Computation-Aware Algorithmic Design for Cyber-Physical Systems, G2484483535, G2574428355, Collaborative Research: CPS: Medium: Constraint Aware Planning and Control for Cyber-Physical Systems, G3510830107, G3556901272, G3936620348, G4112289967, G4341495065, G4516736450, NEW START GRANT, G5932844992, G6098521345, G7452299184, G7583937305, G7780225566, G7801961505, G8289759875, G8876996369
OpenAlex ID: W7148631542