Distributed primal-dual stochastic subgradient algorithms for multi-agent optimization under inequality constraints

作者：Yuan Deming; Xu Shengyuan^*; Zhang Baoyong; Rong Lina

来源：International Journal of Robust and Nonlinear Control, 2013, 23(16): 1846-1868.

DOI：10.1002/rnc.2856

• multi-agent systems
• convex optimization
• subgradient methods
• distributed average consensus
• gossip algorithms

We consider the multi-agent optimization problem where multiple agents try to cooperatively optimize the sum of their local convex objective functions, subject to global inequality constraints and a convex constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the associated Lagrangian function, which can be evaluated with stochastic errors, we propose the distributed primal-dual stochastic subgradient algorithms for two cases: (i) the time model is synchronous and (ii) the time model is asynchronous. In the first case, we obtain bounds on the convergence properties of the algorithm for a diminishing step size. In the second case, for a constant step size, we establish some error bounds on the algorithm's performance. In particular, we prove that the error bounds scale as n root n in the number of n agents.

• 出版日期2013-11-10
• 单位南京大学