Design and analysis for distributed optimization algorithm based on nabla fractional calculus

This paper focuses on the problem of unconstrained distributed optimization over an undirected topological network structure. The difference from the existing continuous time domain distributed optimization algorithms is that nabla fractional calculus is introduced. This improves the algorithm performance of the original literature in terms of iterative complexity of the algorithm. This paper shows that the proposed algorithm is guaranteed to converge to a global minimum of the sum of convex functions on any connected undirected graph, as long as the objective function is convex but not required to be smooth.