Distributed and Robust Fair Optimization Applied to Virus Diffusion Control

This paper proposes three novel nonlinear, continuous-time, distributed algorithms to solve a class of fair resource allocation problems, which allow an interconnected group of operators to collectively minimize a global cost function subject to equality and inequality constraints. The proposed algorithms are designed to be robust so that temporary errors in communication or computation do not change their convergence to the equilibrium, and therefore, operators do not require global knowledge of the total resources in the network nor any specific initialization procedure. To analyze convergence of the algorithms, we use nonlinear analysis tools that exploit partial stability theory and nonsmooth Lyapunov analysis. We illustrate the applicability of our approach in connection to problems of virus spread minimization over computer and public networks. In simulation examples associated with virus spread minimization, we show that the virus elimination algorithms are asymptotically convergent and robust in the proposed sense.