Corrigendum to "Balance of Communication and Convergence: Predefined-time Distributed Optimization Based on Zero-Gradient-Sum"

TL;DR

This paper introduces a distributed optimization algorithm with predefined convergence time, utilizing a sliding manifold and local gradient sharing, effective even with time-varying objectives, and validated through simulations.

Contribution

It presents a novel distributed optimization method that guarantees convergence at a preset time with reduced communication, extending to time-varying functions.

Findings

Algorithm achieves precise convergence at prescribed time.

Requires only primal state sharing, reducing communication.

Effective for time-varying objective functions with local gradient prediction.

Abstract

This paper proposes a distributed optimization algorithm with a convergence time that can be assigned in advance according to task requirements. To this end, a sliding manifold is introduced to achieve the sum of local gradients approaching zero, based on which a distributed protocol is derived to reach a consensus minimizing the global cost. A novel approach for convergence analysis is derived in a unified settling time framework, resulting in an algorithm that can precisely converge to the optimal solution at the prescribed time. The method is interesting as it simply requires the primal states to be shared over the network, which implies less communication requirements. The result is extended to scenarios with time-varying objective function, by introducing local gradients prediction and non-smooth consensus terms. Numerical simulations are provided to corroborate the effectiveness of the proposed algorithms.