1st-Order Dynamics on Nonlinear Agents for Resource Allocation over Uniformly-Connected Networks

TL;DR

This paper introduces a nonlinear first-order consensus-based method for distributed resource allocation that guarantees convergence over weakly-connected networks, accommodating various nonlinearities and physical agent constraints.

Contribution

It presents a generalized nonlinear distributed protocol for convex optimization that ensures convergence under minimal network connectivity assumptions.

Findings

Proves convergence of the nonlinear protocol regardless of nonlinearity type.

Handles physical agent constraints like quantization and saturation.

Works over weakly-connected undirected networks.

Abstract

A general nonlinear $1$st-order consensus-based solution for distributed constrained convex optimization is proposed with network resource allocation applications. The solution is used to optimize continuously-differentiable strictly convex cost functions over weakly-connected undirected networks, while it is anytime feasible and models various nonlinearities to account for imperfections and constraints on the (physical model of) agents in terms of limited actuation capabilities, e.g., quantization and saturation. Due to such inherent nonlinearities, the existing linear solutions considering ideal agent models may not necessarily converge with guaranteed optimality and anytime feasibility. Some applications also impose specific nonlinearities, e.g., convergence in fixed/finite-time or sign-based robust disturbance-tolerant dynamics. Our proposed distributed protocol generalizes such nonlinear models. Putting convex set analysis together with nonsmooth Lyapunov analysis, we prove convergence, (i) regardless of the particular type of nonlinearity, and (ii) with weak network-connectivity requirements (uniform-connectivity).