We present a distributed conjugate gradient method for distributed optimization problems, where each agent computes an optimal solution of the problem locally without any central computation or coordination, while communicating with its immediate, one-hop neighbors over a communication network. Each agent updates its local problem variable using an estimate of the average conjugate direction across the network, computed via a dynamic consensus approach. Our algorithm enables the agents to use uncoordinated step-sizes. We prove convergence of the local variable of each agent to the optimal solution of the aggregate optimization problem, without requiring decreasing step-sizes. In addition, we demonstrate the efficacy of our algorithm in distributed state estimation problems, and its robust counterparts, where we show its performance compared to existing distributed first-order optimization methods.

翻译：本文提出了一种面向分布式优化问题的分布式共轭梯度法。在该方法中，每个智能体无需中心计算或协调，仅通过与通信网络中的直接单跳邻居交互，即可独立计算问题的最优局部解。各智能体利用动态一致性方法估计网络中的平均共轭方向，并据此更新其局部问题变量。本算法允许智能体采用非协调的步长。我们证明，在不要求递减步长的条件下，每个智能体的局部变量均收敛至全局优化问题的最优解。此外，我们通过分布式状态估计问题及其鲁棒扩展问题，验证了本算法的有效性，并与现有分布式一阶优化方法进行了性能对比。