Distributed Optimization of Multiagent Systems Subject to Inequality Constraints
Distributed Optimization of Multiagent Systems Subject to Inequality Constraints
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DOI：
10.1109/tcyb.2019.2927725
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发表时间：
2019-07
影响因子：
11.8
通讯作者：
F. Tian;Wenwu Yu;Junjie Fu;W. Gu;Juping Gu
中科院分区：
文献类型：
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作者：
F. Tian;Wenwu Yu;Junjie Fu;W. Gu;Juping Gu
本文研究了一类带不等式约束的分布式凸优化问题。每个代理与其成本函数相关联，并且只能与其邻居交换信息。假设每个成本函数都是凸的，并且最优化变量受一个不等式约束。目标是使所有的智能体达成共识，同时收敛到局部成本函数和的最小点。提出了一种分布式协议，保证所有智能体在有限时间内达成一致，并在不等约束条件下收敛到最优点。基于参数投影的思想，该协议包括两个像样的方向。一种是使代价函数减小，另一种是使智能体向约束集迈进。结果表明，该协议无需使用拉格朗日乘子技术，即可在连通无向图下解决该问题。特别地，所有的智能体都能在有限的时间内到达约束集并停留在约束集上。该方法也可用于集中优化问题。
In this paper, we study a distributed convex optimization problem with inequality constraints. Each agent is associated with its cost function, and can only exchange information with its neighbors. It is assumed that each cost function is convex and the optimization variable is subject to an inequality constraint. The objective is to make all the agents reach consensus, and meanwhile converge to the minimum point of the sum of local cost functions. A distributed protocol is proposed to guarantee that all agents can reach consensus in finite time and converge to the optimal point within the inequality constraints. Based on the ideas of parameter projection, the protocol includes two decent directions. One makes the cost function decrease, and the other makes agents step forward to the constraint set. It is shown that the proposed protocol solves the problem under connected undirected graphs without using a Lagrange multiplier technique. Especially, all of the agents could reach the constraint sets in finite time and stay in there after. The method could also be used in the centralized optimization problems.