We study distributed convex constrained optimization on a time-varying multi-agent network. Each agent has access to its own local cost function, its local constraints, and its instant number of out-neighbors. The collective goal is to minimize the sum of the cost functions over the set of all constraints. We utilize the push-sum protocol to be able to solve this distributed optimization problem. We adapt the push-sum optimization algorithm, which has been studied in context of unconstrained optimization so far, to convex constrained optimization by introducing an appropriate choice of penalty functions and penalty parameters. Under some additional technical assumptions on the gradients we prove convergence of the distributed penalty-based push-sum algorithm to the optimal value of the global objective function. We apply the proposed penalty-based push-sum algorithm to the problem of distributed energy management in smart grid and discuss the advantages of this novel procedure in comparison with existing ones.
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机译：我们研究了在时变多代理网络上的分布式凸起约束优化。每个代理都可以访问自己的本地成本函数，其本地约束及其即时数量。集体目标是最小化所有约束集中的成本函数的总和。我们利用推送协议能够解决这个分布式优化问题。 We adapt the push-sum optimization algorithm, which has been studied in context of unconstrained optimization so far, to convex constrained optimization by introducing an appropriate choice of penalty functions and penalty parameters.在梯度的一些额外技术假设下，我们将分布式惩罚的推送算法的融合证明了全局目标函数的最佳值。我们将建议的基于罚款的推挽算法应用于智能电网中分布式能源管理问题，并与现有的新方法讨论了这种新方法的优势。
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