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

A general nonlinear 1st-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 net-works, while it is anytime feasible and models various non-linearities to account for imperfections and constraints on the (physical model of) agents in terms of limited actuation capa-bilities, 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 im-pose specific nonlinearities, e.g., convergence in fixed/finite-time or sign-based robust disturbance-tolerant dynamics. Our pro-posed 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).