Discrete-Time Algorithm for Distributed Unconstrained Optimization Problem With Finite-Time Computations

Abstract

This brief investigates the distributed unconstrained optimization problem, where its global objective function consists of the sum of $N$ local objective functions. The aim for this brief is to design a discrete-time algorithm to solve the considered distributed optimization problem using only local computations and local information exchanges. To this end, a discrete-time algorithm resorting to the conjugate gradient method is proposed, and by it, the optimal solution to a class of distributed optimization problems over a static undirected graph can be obtained with finite-time computations under some mild conditions. Furthermore, simulations are given to verify the validity of the designed algorithm.