A Fixed-Time Convergent Distributed Algorithm for Strongly Convex Functions in a Time-Varying Network

This paper presents a novel distributed nonlinear protocol for minimizing the sum of convex objective functions in a fixed time under time-varying communication topology. In a distributed setting, each node in the network has access only to its private objective function, while exchange of local information, such as, state and gradient values, is permitted between the immediate neighbors. Earlier work in literature considers distributed optimization protocols that achieve convergence of the estimation error in a finite time for static communication topology, or under specific set of initial conditions. This study investigates first such protocol for achieving distributed optimization in a fixed time that is independent of the initial conditions, for time-varying communication topology. Numerical examples corroborate our theoretical analysis.