This paper introduces a distributed continuous-time algorithm that utilizes dual consensus to tackle the optimization problem involving time-varying (TV) local objective functions and TV coupled equality constraint. Here, the local objective functions can be any strongly convex functions. The optimum solution is represented by a trajectory rather than a fixed point, owing to the dynamic nature of the objective functions and the constraint. The initial step involves converting the studied problem into an equivalent saddle-point problem. Subsequently, we provide the optimal conditions for this transformed problem. Then a distributed continuous-time algorithm based on dual consensus is provided, guaranteeing that all agents possess the capability to discover and follow the optimal TV trajectories. It is noticeable that there are no limitations imposed on the information regarding local objective functions and the coupled equality constraint except for the strongly convexity of local objective functions. In addition, two simulation instances and the comparisons with state-of-the-art methods are performed in order to validate the proposed algorithm.

中文翻译：

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耦合等式约束时变优化的分布式双一致性算法

本文介绍了一种分布式连续时间算法，该算法利用双重共识来解决涉及时变（TV）局部目标函数和TV耦合等式约束的优化问题。这里，局部目标函数可以是任何强凸函数。由于目标函数和约束的动态性质，最优解由轨迹而不是固定点表示。第一步涉及将所研究的问题转换为等效的鞍点问题。随后，我们为这个转化问题提供了最佳条件。然后提供了一种基于双重共识的分布式连续时间算法，保证所有代理都具有发现并遵循最优电视轨迹的能力。值得注意的是，除了局部目标函数的强凸性之外，关于局部目标函数和耦合等式约束的信息没有受到任何限制。此外，还进行了两个仿真实例并与最先进的方法进行比较，以验证所提出的算法。