# Distributed Finite-Sum Constrained Optimization subject to Nonlinearity on the Node Dynamics

arXiv: https://arxiv.org/abs/2203.14527 · HTML: https://mlsanity.com/paper/2203.14527/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [An improved convergence analysis for decentralized online stochastic non-convex optimization](https://mlsanity.com/paper/2008.04195/) (2020)
- [A general framework for decentralized optimization with first-order methods](https://mlsanity.com/paper/2009.05837/) (2020)
- [Distributed heavy-ball: A generalization and acceleration of first-order methods with gradient tracking](https://mlsanity.com/paper/1808.02942/) (2018)
- [Accelerated Decentralized Optimization with Local Updates for Smooth and Strongly Convex Objectives](https://mlsanity.com/paper/1810.02660/) (2018)
- [Fixed-Time Stable Gradient Flows: Applications to Continuous-Time Optimization](https://mlsanity.com/paper/1808.10474/) (2018)
- [Distributed support-vector-machine over dynamic balanced directed networks](https://mlsanity.com/paper/2104.00399/) (2021)
- [Fast-Convergent Dynamics for Distributed Allocation of Resources Over Switching Sparse Networks with Quantized Communication Links](https://mlsanity.com/paper/2012.08181/) (2020)
- [Single-Bit Consensus with Finite-Time Convergence: Theory and Applications](https://mlsanity.com/paper/2001.00141/) (2020)
- [Tracking-ADMM for Distributed Constraint-Coupled Optimization](https://mlsanity.com/paper/1907.10860/) (2019)
- [Optimal CPU Scheduling in Data Centers via a Finite-Time Distributed Quantized Coordination Mechanism](https://mlsanity.com/paper/2104.03126/) (2021)
- [1st-Order Dynamics on Nonlinear Agents for Resource Allocation over Uniformly-Connected Networks](https://mlsanity.com/paper/2109.04822/) (2021)
- [Distributed Resource Allocation on Dynamic Networks in Quadratic Time](https://mlsanity.com/paper/1507.07850/) (2015)

## Abstract (arXiv)

Motivated by recent development in networking and parallel data-processing, we consider a distributed and localized finite-sum (or fixed-sum) allocation technique to solve resource-constrained convex optimization problems over multi-agent networks (MANs). Such networks include (smart) agents representing an intelligent entity capable of communication, processing, and decision-making. In particular, we consider problems subject to practical nonlinear constraints on the dynamics of the agents in terms of their communications and actuation capabilities (referred to as the node dynamics), e.g., networks of mobile robots subject to actuator saturation and quantized communication. The considered distributed sum-preserving optimization solution further enables adding purposeful nonlinear constraints, for example, sign-based nonlinearities, to reach convergence in predefined-time or robust to impulsive noise and disturbances in faulty environments. Moreover, convergence can be achieved under minimal network connectivity requirements among the agents; thus, the solution is applicable over dynamic networks where the channels come and go due to the agent's mobility and limited range. This paper discusses how various nonlinearity constraints on the optimization problem (e.g., collaborative allocation of resources) can be addressed for different applications via a distributed setup (over a network).