A distributed continuous-time modified Newton–Raphson algorithm. (February 2022)

• Record Type: Journal Article
• Authors: Moradian, Hossein; Kia, Solmaz S.
• Is Part Of: Automatica. Volume 136(2022)
• Publication Date: 2022-02
• Subjects: Distributed optimization -- Newton–Raphson method -- Convex optimization -- Machine learning; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109886
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the continuous-time Newton–Raphson method, however structurally, it is amenable to a more efficient distributed implementation. We present a distributed implementation of our proposed optimization algorithm and prove its convergence via Lyapunov analysis. A numerical example demonstrates our results.