# Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication

arXiv: https://arxiv.org/abs/1401.4432 · HTML: https://mlsanity.com/paper/1401.4432/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2014.

## Built on by (most cited first, 11 of 11)

- [Asynchronous Upper Confidence Bound Algorithms for Federated Linear Bandits](https://mlsanity.com/paper/2110.01463/) (2021)
- [Improving the Transient Times for Distributed Stochastic Gradient Methods](https://mlsanity.com/paper/2105.04851/) (2021)
- [Distributed Random Reshuffling over Networks](https://mlsanity.com/paper/2112.15287/) (2021)
- [On Centralized and Distributed Mirror Descent: Convergence Analysis Using Quadratic Constraints](https://mlsanity.com/paper/2105.14385/) (2021)
- [Communication Efficient ConFederated Learning: An Event-Triggered SAGA Approach](https://mlsanity.com/paper/2402.18018/) (2024)
- [Quantization Avoids Saddle Points in Distributed Optimization](https://mlsanity.com/paper/2403.10423/) (2024)
- [A primal-dual perspective for distributed TD-learning](https://mlsanity.com/paper/2310.00638/) (2023)
- [On Linear Convergence of PI Consensus Algorithm under the Restricted Secant Inequality](https://mlsanity.com/paper/2310.00419/) (2023)
- [Distributed Optimization via Kernelized Multi-armed Bandits](https://mlsanity.com/paper/2312.04719/) (2023)
- [Revisiting Multi-Agent Asynchronous Online Optimization with Delays: the Strongly Convex Case](https://mlsanity.com/paper/2503.10013/) (2025)
- [Quantized Stochastic Primal-Dual Methods for Distributed Optimization under Relaxed Global Geometry](https://mlsanity.com/paper/2606.11339/) (2026)

## Abstract (arXiv)

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. When the local cost functions are convex and the global cost function is strictly convex, we establish asymptotic convergence under connected graph topologies. We also characterize the algorithm's correctness under time-varying interaction topologies and study its privacy preservation properties. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication. Building on this result, we design a provably-correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results.