IEEE Trans Syst Man Cybern B Cybern. 2011 Dec;41(6):1715-24. doi: 10.1109/TSMCB.2011.2160394. Epub 2011 Aug 4.
This paper studies the problem of optimizing the sum of multiple agents' local convex objective functions, subject to global convex inequality constraints and a convex state constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the Lagrangian function associated with the problem, we propose a distributed algorithm, named the distributed primal-dual subgradient method, to provide approximate saddle points of the Lagrangian function, based on the distributed average consensus algorithms. Under Slater's condition, we obtain bounds on the convergence properties of the proposed method for a constant step size. Simulation examples are provided to demonstrate the effectiveness of the proposed method.
本文研究了在网络上，在全局凸不等式约束和凸状态约束集的条件下，优化多个智能体局部凸目标函数之和的问题。通过将原始和对偶最优解表征为与该问题相关的拉格朗日函数的鞍点，我们基于分布式平均共识算法，提出了一种名为分布式原始对偶次梯度法的分布式算法，以提供拉格朗日函数的近似鞍点。在斯莱特条件下，我们得到了该方法在固定步长下收敛性质的界。提供了仿真示例来证明所提方法的有效性。
