期刊
IEEE TRANSACTIONS ON CYBERNETICS
卷 51, 期 4, 页码 2232-2241出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2019.2927725
关键词
Multi-agent systems; Cost function; Protocols; Convergence; Convex functions; Heuristic algorithms; Distributed optimization; finite-time consensus; inequality constraints; multiagent systems; parameter projection
类别
资金
- National Natural Science Foundation of China [61673107]
- National Ten Thousand Talent Program for Young Top-Notch Talents [W2070082]
- Cheung Kong Scholars Programme of China for Young Scholars [Q2016109]
- Jiangsu Provincial Key Laboratory of Networked Collective Intelligence [BM2017002]
This paper studies a distributed convex optimization problem with inequality constraints and proposes a distributed protocol to ensure all agents reach consensus and converge to the optimal point within the constraints in finite time. The protocol utilizes the idea of parameter projection, including two decent directions, to update information according to specific rules.
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.
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