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This paper focuses on a distributed coupled constrained convex optimizationproblem over directed unbalanced and time-varying multi-agent networks, wherethe global objective function is the sum of all agents' private local objectivefunctions, and decisions of all agents are subject to coupled equality andinequality constraints and a compact convex subset. In the multi-agentnetworks, each agent exchanges information with other neighboring agents.Finally, all agents reach a consensus on decisions, meanwhile achieving thegoal of minimizing the global objective function under the given constraintconditions. For the purpose of protecting the information privacy of eachagent, we first establish the saddle point problem of the constrained convexoptimization problem considered in this article, then based on the push-pullmethod, develop a distributed primal-dual algorithm to solve the dual problem.Under Slater's condition, we will show that the sequence of points generated bythe proposed algorithm converges to a saddle point of the Lagrange function.Moreover, we analyze the iteration complexity of the algorithm.

Push-Pull Based Distributed Primal-Dual Algorithm for Coupled Constrained Convex Optimization in Multi-Agent Networks