Distributed Anytime-Feasible Resource Allocation subject to Heterogeneous Time-Varying Delays

This paper considers distributed allocation strategies, formulated as a distributed sum-preserving (fixed-sum) allocation of resources over a multi-agent network in the presence of heterogeneous arbitrary time-varying delays. We propose a double time-scale scenario for unknown delays and a faster single time-scale scenario for known delays. Further, the links among the nodes are considered subject to certain nonlinearities (e.g, quantization and saturation/clipping). We discuss different models for nonlinearities and how they may affect the convergence, sum-preserving feasibility constraint, and solution optimality over general weight-balanced uniformly strongly connected networks and, further, time-delayed undirected networks. Our proposed scheme works in a variety of applications with general non-quadratic strongly-convex smooth objective functions. The non-quadratic part, for example, can be due to additive convex penalty or barrier functions to address the local box constraints. The network can change over time, is not necessarily connected at all times, but is only assumed to be uniformly-connected. The novelty of this work is to address all-time feasible Laplacian gradient solutions in presence of nonlinearities, switching digraph topology (not necessarily all-time connected), and heterogeneous time-varying delays.