A Fast Finite-Time Consensus based Gradient Method for Distributed Optimization over Digraphs

In this paper, we study the unconstrained optimization problem in a distributed way over directed strongly connected communication graphs. We propose an algorithm, which combines techniques of both gradient descent (GD) and finite-time exact ratio consensus (FTERC). Different from the techniques of average or dynamic average consensus with asymptotic convergence or techniques of finite-time "approximate" consensus with inexact accuracy in the literature, with the help of FTERC for gradient tracking, our proposed distributed FTERC based GD algorithm has a faster convergence rate related to the optimization iteration number and a larger step-size upper bound compared with other algorithms, as demonstrated in the simulations.