Distributed discrete‐time optimization algorithms with applications to resource allocation in epidemics control

Abstract

SummaryThis work presents and analyzes 2 novel distributed discrete‐time nonlinear algorithms to solve a class of decentralized resource allocation problems. The algorithms allow an interconnected group of agents to collectively minimize a global cost function under inequality and equality constraints. Under some technical conditions, it is shown that the first proposed algorithm converges asymptotically to the desired equilibrium, while the second one converges to the solution in a practical way as long as the stepsize chosen is sufficiently small. Of particular interest is that the algorithms are designed to be robust to temporary errors in communication or computation. In addition, agents do not require global knowledge of total resources in the network or any specific procedure for initialization and the cost function is not required to be separable. The convergence of the algorithms is established via nonsmooth Lyapunov analysis. Finally, we illustrate the applicability of our strategies on a virus mitigation problem over computer and human networks.