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

TL;DR

This paper introduces a distributed finite-sum optimization method for multi-agent networks that handles nonlinear constraints and node dynamics, enabling robust and fast convergence even in dynamic, resource-limited environments.

Contribution

It presents a novel distributed optimization framework that incorporates nonlinear node dynamics and constraints, ensuring convergence under minimal network connectivity.

Findings

Enables convergence with nonlinear constraints like saturation and quantization.

Achieves predefined-time convergence and robustness to noise.

Operates effectively over dynamic, intermittently connected networks.

Abstract

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).