A Finite-Time Protocol for Distributed Time-Varying Optimization Over a Graph

In this paper we address a time-varying quadratic optimization problem over graph under the assumption that shares same sparsity pattern as static encoding undirected network topology which multi-agent systems interacts. Notably, framework allows to effectively model scenarios in is inherently embedded within topology, e.g., flow balancing, electrical power system managements or packet routing problems. regard, propose finite-time distributed algorithm track optimal solution time. Specifically, first solve frozen-time problem, providing necessary and sufficient condition for be globally optimal. Then, based on such condition, continuous-time nonsmooth developed. Numerical simulations are provided corroborate theoretical findings.