Nabla Fractional Distributed Optimization Algorithm Over Unbalanced Graphs
X. Hong, Yiheng Wei, Shuaiyu Zhou, Dongdong Yue, Jinde Cao · IEEE Control Systems Letters · 2024
While fractional calculus has shown appealing properties in optimization related fields, few results have been reported on distributed optimization with fractional dynamics over networks. In this letter, we propose a novel Nabla fractional distributed optimization algorithm over unbalanced graphs. Rigorous analysis demonstrates that the proposed algorithm converges at least with the Mittag—Leffler rate, achieving a globally optimal solution. The algorithm’s effectiveness is validated through numerical simulations. The research underscores the potential of utilizing Nabla fractional difference to improve the efficiency of distributed optimization algorithms.