  This paper focuses on distributed constrained optimization over time-varying
directed networks, where all agents cooperate to optimize the sum of their
locally accessible objective functions subject to a coupled inequality
constraint consisting of all their local constraint functions. To address this
problem, we develop a buffering drift-plus-penalty algorithm, referred to as
B-DPP. The proposed B-DPP algorithm utilizes the idea of drift-plus-penalty
minimization in centralized optimization to control constraint violation and
objective error, and adapts it to the distributed setting. It also innovatively
incorporates a buffer variable into local virtual queue updates to acquire
flexible and desirable tracking of constraint violation. We show that B-DPP
achieves $O(1/\sqrt{t})$ rates of convergence to both optimality and
feasibility, which outperform the alternative methods in the literature.
Moreover, with a proper buffer parameter, B-DPP is capable of reaching
feasibility within a finite number of iterations, which is a pioneering result
in the area. Simulations on a resource allocation problem over 5G virtualized
networks demonstrate the competitive convergence performance and efficiency of
B-DPP.
