Distributed and robust resource allocation algorithms for multi-agent systems via discrete-time iterations

This paper proposes two novel nonlinear discrete-time distributed algorithms to solve a class of resource allocation problems. The proposed algorithms allow an interconnected group of agents to collectively minimize a global cost function subject to equality and inequality constraints. Under some technical conditions, we show that the algorithms converge to the solution in a practical way as long as the stepsize chosen is sufficiently small. Of particular interest is that the proposed algorithms are designed to be robust so that temporary errors in communication or computation do not change their convergence to a neighborhood around the equilibrium, and to this end, agents do not require global knowledge of total resources in the network or any specific procedure for initialization. The convergence of the algorithms is established via second-order convexity theory together with nonsmooth Lyapunov analysis. To illustrate the applicability of our strategies, we study a virus mitigation problem over computer and human networks.