A Unified Framework for Nabla Fractional Distributed Optimization Algorithms

This paper investigates the framework construction problem for discrete time distributed optimization algorithms. Since the consensus optimization task can be decomposed into consensus and optimality components, the framework proposed in this paper consists of a consensus estimator that ensures convergence and an optimizer that ensures optimality. Notably, this framework not only encompasses integer algorithms but also applies to fractional algorithms. Several existing algorithms are reorganized via the framework and several new algorithms are further proposed. Finally, the illustrative example is provided to validate the effectiveness of the elaborated algorithms.