An accelerated distributed method with inexact model of relative smoothness and strong convexity

Abstract

Distributed optimisation methods are widely applied in many systems where agents cooperate with each other to minimise a sum-type problem over a connected network. An accelerated distributed method based on the inexact model of relative smoothness and strong convexity is introduced by the authors. The authors demonstrate that the proposed method can converge to the optimal solution at the linear rate $\frac{1}{{\left(1+1/\left(4\sqrt{{\kappa }_g}\right)\right)}^2}$ and achieve the optimal gradient computation complexity and the near optimal communication complexity, where κ_g denotes the global condition number. Finally, the numerical experiments are provided to validate the theoretical results and further show the efficacy of the proposed method.