Nabla Fractional Distributed Optimization Algorithm Over Unbalanced Graphs

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.