In this note, a distributed subgradient-based algorithm is proposed for continuous-time multi-agent systems to search a feasible solution to convex inequalities. The algorithm involves each agent achieving a state constrained by its own inequalities while exchanging local information with other agents under a time-varying directed communication graph. With the validity of a mild connectivity condition associated with the communication graph, it is shown that all agents will reach agreement asymptotically and the consensus state is in the solution set of the inequalities. Furthermore, the method is also extended to solving the distributed optimization problem of minimizing the sum of local objective functions subject to convex inequalities. Simulation examples are presented to demonstrate the effectiveness of the theoretical results.

中文翻译：

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求解凸不等式的分布式算法


在本文中，提出了一种基于分布式次梯度的算法，用于连续时间多智能体系统，以搜索凸不等式的可行解。该算法涉及每个代理实现受其自身不等式约束的状态，同时在时变有向通信图下与其他代理交换本地信息。随着与通信图相关的温和连接条件的有效性，表明所有代理将渐近地达成一致，并且共识状态位于不等式的解集中。此外，该方法还扩展到求解最小化受凸不等式影响的局部目标函数之和的分布式优化问题。仿真实例验证了理论结果的有效性。