# Distributed Convex Optimization for Continuous-Time Dynamics with Time-Varying Cost Function

arXiv: https://arxiv.org/abs/1507.04878 · HTML: https://mlsanity.com/paper/1507.04878/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2015.

## Built on by (most cited first, 8 of 8)

- [Distributed support-vector-machine over dynamic balanced directed networks](https://mlsanity.com/paper/2104.00399/) (2021)
- [First-Order Dynamic Optimization for Streaming Convex Costs](https://mlsanity.com/paper/2310.07925/) (2023)
- [Time-Varying Optimization for Streaming Data Via Temporal Weighting](https://mlsanity.com/paper/2510.13052/) (2025)
- [Distributed Unconstrained Optimization with Time-varying Cost Functions](https://mlsanity.com/paper/2212.09472/) (2022)
- [D-SVM over Networked Systems with Non-Ideal Linking Conditions](https://mlsanity.com/paper/2304.06667/) (2023)
- [Communication-Efficient Zeroth-Order Distributed Online Optimization: Algorithm, Theory, and Applications](https://mlsanity.com/paper/2306.05655/) (2023)
- [Time-Varying Convex Optimization with O(n) Computational Complexity](https://mlsanity.com/paper/2410.15009/) (2024)
- [Distributed Optimization with Streaming Data: A Temporal Weighting Perspective](https://mlsanity.com/paper/2608.09565/) (2026)

## Abstract (arXiv)

In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. Two discontinuous algorithms based on the signum function are proposed to solve the problem in each case. Then in the case of double-integrator dynamics, two continuous algorithms based on, respectively, a time-varying and a fixed boundary layer are proposed as continuous approximations of the signum function. Also, to account for inter-agent collision for physical agents, a distributed convex optimization problem with swarm tracking behavior is introduced for both single-integrator and double-integrator dynamics.