2019/05/27 by Tatiana Tatarenko, Jan Zimmermann, Tatarenko, Tatiana +3
Computer Science · #Distributed Control Multi-Agent Systems #Stochastic Gradient Optimization Techniques #Cooperative Communication and Network Coding
paper · pdf · doi:10.48550/arxiv.1905.11104
We study distributed convex constrained optimization on a time-varying\nmulti-agent network. Each agent has access to its own local cost function, its\nlocal constraints, and its instant number of out-neighbors. The collective goal\nis to minimize the sum of the cost functions over the set of all constraints.\nWe utilize the push-sum protocol to be able to solve this distributed\noptimization problem. We adapt the push-sum optimization algorithm, which has\nbeen studied in context of unconstrained optimization so far, to convex\nconstrained optimization by introducing an appropriate choice of penalty\nfunctions and penalty parameters. Under some additional technical assumptions\non the gradients we prove convergence of the distributed penalty-based push-sum\nalgorithm to the optimal value of the global objective function. We apply the\nproposed penalty-based push-sum algorithm to the problem of distributed energy\nmanagement in smart grid and discuss the advantages of this novel procedure in\ncomparison with existing ones.\n