Finite-time Distributed ConvexOptimization with Zero-Gradient-Sum Algorithms

Abstract

This article considers the distributed finite-time optimization problem of multi-agent systems within the Zero-Gradient-Sum (ZGS) framework. We employ a distributed algorithm to drive the estimate of each agent to converge to the optimal solution of the global objective function, the sum of the local objectives. In a general case with non-quadratic local functions, we can obtain a finite-time convergence. Furthermore, when all the local cost functions are quadratic, the proposed algorithm can achieve a fixed-time result such that the upper bound of settling time can be estimated regardless of the initial conditions. Considering that the communication network may be affected by some external disturbances, we also extend to consider the case with switching topologies. Finally, the algorithms are demonstrated via an example simulation.