摘要
This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations.Firstly,the authors proposed“Consensus+Projection”flow with fractional order dynamics,which has more design freedom and the potential to obtain a better convergent performance than that of conventional first order algorithms.Moreover,the authors prove that the proposed algorithm is convergent under certain iteration order and step-size.Furthermore,the authors develop iteration order switching scheme with initial condition design to improve the convergence performance of the proposed algorithm.Finally,the authors illustrate the effectiveness of the proposed method with several numerical examples.
基金
supported by the National Natural Science Foundation of China under Grant Nos.62103003,62073001,and 61973002
the Anhui Provincial Key Research and Development Project under Grant2022i01020013
the University Synergy Innovation Program of Anhui Province under Grant No.GXXT-2021-010
the Anhui Provincial Natural Science Foundation under Grant No.2008085J32
the National Postdoctoral Program for Innovative Talents under Grant No.BX20180346
the General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2019M660834。
