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This paper studies the distributed optimization problem with possiblynonidentical local constraints, where its global objective function is composedof $N$ convex functions. The aim is to solve the considered optimizationproblem in a distributed manner over time-varying unbalanced directedtopologies by using only local information and performing only localcomputations. Towards this end, a new distributed discrete-time algorithm isdeveloped by synthesizing the row stochastic matrices sequence and columnstochastic matrices sequence analysis technique. Furthermore, for the developeddistributed discrete-time algorithm, its convergence property to the optimalsolution as well as its convergence rate are established under some mildassumptions. Numerical simulations are finally presented to verify thetheoretical results.

Distributed Algorithm Over Time-Varying Unbalanced Topologies for Optimization Problem Subject to Multiple Local Constraints