This paper considers solving distributed convex optimization problems in peer-to-peer multi-agent networks. The network is assumed to be synchronous and connected. By using the proportional-integral (PI) control strategy, various algorithms with fixed stepsize have been developed. The earliest among them is the PI consensus algorithm. Using Lyapunov theory, we guarantee exponential convergence of the PI consensus algorithm for restricted strongly convex functions with rate-matching discretization, without requiring convexity of individual local cost functions, for the first time. In order to accelerate the PI consensus algorithm, we incorporate local pre-conditioning in the form of constant positive definite matrices and numerically validate its efficiency compared to the prominent distributed convex optimization algorithms. Unlike classical pre-conditioning, where only the gradients are multiplied by a pre-conditioner, the proposed pre-conditioning modifies both the gradients and the consensus terms, thereby controlling the effect of the communication graph between the agents on the PI consensus algorithm.

该研究通过使用比例积分（PI）控制策略，在同步连接的点对点多智能体网络中解决分布式凸优化问题。它提出了PI共识算法，利用Lyapunov理论保证了限制强凸函数具有速率匹配离散化的PI共识算法的指数收敛性。为了加速PI共识算法，引入了本地预处理形式的常数正定矩阵，与其他分布式凸优化算法相比，其有效性得到了数值验证。与传统预处理不同，该预处理同时修改了梯度和共识项，从而控制了智能体之间通信图对PI共识算法的影响。

受限强凸性下的预条件PI一致性算法的线性收敛