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首页> 外文期刊>IEEE Transactions on Automatic Control >Continuous-Time Distributed Subgradient Algorithm for Convex Optimization With General Constraints
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Continuous-Time Distributed Subgradient Algorithm for Convex Optimization With General Constraints

机译：具有一般约束的凸优化的连续时间分布式次梯度算法

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摘要

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch-Kuhn-Tucker condition. By using tools from nonsmooth analysis and set-valued function theory. it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis.
机译：针对具有一般约束的任何固定和连接网络，研究了分布式凸优化问题。为了解决这一优化问题，提出了一种基于Karuch-Kuhn-Tucker条件的新型连续时间分布式次梯度优化算法。通过使用来自非平滑分析和集值函数理论的工具。实践证明，在装有所设计算法的Agent网络上可以解决分布式凸优化问题。对于目标函数是凸而不是严格凸的情况，证明了与最优变量关联的主体的状态可以收敛到优化问题的最优解。对于目标函数严格凸的情况，进一步表明与最优变量相关的主体状态可以收敛到唯一最优解。最后，进行了一些仿真来说明理论分析。

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