This paper studies distributed convex optimization problems over continuous-time multiagent networks subject to two types of constraints, i.e., local feasible set constraints and coupled inequality constraints, where all involved functions are not necessarily differentiable, only assumed to be convex. In order to solve this problem, a modified primal-dual continuous-time algorithm is proposed by projections on local feasible sets. With the aid of constructing a proper Lyapunov function candidate, the existence of solutions of the algorithm in the Carathéodory sense and the convergence of the algorithm to an optimal solution for the distributed optimization problem are established. Additionally, a sufficient condition is provided for making the algorithm fully distributed. Finally, the theoretical result is corroborated by a simulation example.

中文翻译：

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耦合不等式约束的分布式连续时间非光滑凸优化

本文研究了连续时间多主体网络上的分布式凸优化问题，该问题受两种约束的约束，即局部可行集约束和不等式约束，其中所有涉及的函数不一定都是可微的，而仅假定为凸的。为了解决这个问题，通过对局部可行集进行投影，提出了一种改进的原始-对偶连续时间算法。借助于构造适当的Lyapunov函数候选，建立了Carathéodory意义上算法的解的存在性以及该算法对分布式优化问题的最优解的收敛性。另外，提供了充分的条件以使算法完全分布。最后，通过仿真实例验证了理论结果。