Distributed Saddle-Point Subgradient Algorithms With Laplacian Averaging

作者：Mateos Nunez David^*; Cortes Jorge

来源：IEEE Transactions on Automatic Control, 2017, 62(6): 2720-2735.

DOI：10.1109/TAC.2016.2616646

• Distributed optimization
• Laplacian averaging
• multi-agent networks
• saddle-point algorithms

We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a sum of convex functions in the local variables of the agents. In the latter case, the proposed algorithm reduces to primal-dual updates using local subgradients and Laplacian averaging on local copies of the multipliers associated to the global constraints. For the case of general convex-concave saddle-point problems, our analysis establishes the convergence of the running time-averages of the local estimates to a saddle point under periodic connectivity of the communication digraphs. Specifically, choosing the gradient step-sizes in a suitable way, we show that the evaluation error is proportional to 1/root t, where t is the iteration step. We illustrate our results in simulation for an optimization scenario with nonlinear constraints coupling the decisions of agents that cannot communicate directly.

• 出版日期2017-6