  This paper studies the distributed optimization problem with possibly
nonidentical local constraints, where its global objective function is composed
of $N$ convex functions. The aim is to solve the considered optimization
problem in a distributed manner over time-varying unbalanced directed
topologies by using only local information and performing only local
computations. Towards this end, a new distributed discrete-time algorithm is
developed by synthesizing the row stochastic matrices sequence and column
stochastic matrices sequence analysis technique. Furthermore, for the developed
distributed discrete-time algorithm, its convergence property to the optimal
solution as well as its convergence rate are established under some mild
assumptions. Numerical simulations are finally presented to verify the
theoretical results.
