A Distributed Penalty Algorithm for Resource Allocation over Digraphs

This paper studies the distributed resource allocation problem with coupled equality constraints and local inequality constraints over digraphs. To solve this problem, we design a new distributed continuous-time penalty algorithm, where a penalty function method is introduced to tackle the local inequality constraints. Compared with the existing related results, the proposed algorithm does not rely on specific initial conditions and can drive the decision variables of agents to converge to the optimal solution even on unbalanced digraphs. Moreover, the convergence properties of the proposed scheme are provided and proved. Finally, a numerical simulation is provided to demonstrate our scheme.