This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need not be convex as long as the global cost function is strongly convex and (ii) the convergence rate of the distributed algorithm is arbitrarily close to the convergence rate of the centralized one. Two particular continuous-time algorithms are presented using the proportional-integral-type couplings. One has benefit of `initialization-free,' so that agents can join or leave the network during the operation. The other one has the minimal amount of communication information. After presenting a general theorem that can be used for designing distributed algorithms, we particularly present a distributed heavy-ball method and discuss its strength over other methods.

中文翻译：

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混合动力学方法的分布式优化：总和凸性和收敛速度

本文研究了混合动力学方法在分布式优化问题中的应用，其中全局成本函数由局部成本函数之和给出。好处包括（i）只要全局成本函数是强凸的，个体成本函数就不必是凸的；以及（ii）分布式算法的收敛率可以任意地接近集中式算法的收敛率。使用比例积分型耦合给出了两种特殊的连续时间算法。一个优点是“无需初始化”，因此代理可以在操作过程中加入或离开网络。另一个具有最少的通信信息。提出了可用于设计分布式算法的一般性定理之后，