Nabla fractional distributed optimization algorithm with directed communication topology

This paper proposes a fractional order distributed optimization algorithm for balanced directed graphs by introducing nabla fractional calculus. The proposed algorithm is shown to converge at the rate of Mittag-Leffler to the exact solution of the distributed optimization problem on balanced connected digraph topological network structure with strong convex and smooth objective function. A numerical example is provided to verify the effectiveness of the algorithm and demonstrate the potential of fractional calculus in addressing distributed optimization problems.