Distributed stopping criteria for the power iteration applied to virus mitigation

This paper proposes a novel distributed stopping criterion for the well-known Power Iteration method for symmetric Metzler matrices. We provide a bound on the accuracy of the approximations for the maximum eigenvalue of the matrix and its corresponding eigenvector. We apply our result to mitigate virus spreading over a complex network by interconnecting the Power Iteration algorithm together with our recently developed ROBUST BOX-CONSTRAINED GRADIENT FAIRNESS algorithm. This distributed algorithm allows an interconnected group of agents to collectively minimize a global cost function subject to equality and inequality constraints. The Power Iteration and the distributed stopping criterion provides an approximation of the cost functions gradient for each iteration. We show that the interconnection between the two methods is convergent and preserves the convergence properties of the ROBUST BOX-CONSTRAINED GRADIENT FAIRNESS algorithm.