  This paper aims to address distributed optimization problems over directed
and time-varying networks, where the global objective function consists of a
sum of locally accessible convex objective functions subject to a feasible set
constraint and coupled inequality constraints whose information is only
partially accessible to each agent. For this problem, a distributed
proximal-based algorithm, called distributed proximal primal-dual (DPPD)
algorithm, is proposed based on the celebrated centralized proximal point
algorithm. It is shown that the proposed algorithm can lead to the global
optimal solution with a general stepsize, which is diminishing and
non-summable, but not necessarily square-summable, and the saddle-point running
evaluation error vanishes proportionally to $O(1/\sqrt{k})$, where $k>0$ is the
iteration number. Finally, a simulation example is presented to corroborate the
effectiveness of the proposed algorithm.
