A Second-Order Multi-Agent Network for Bound-Constrained Distributed Optimization

• Published in: IEEE transactions on automatic control Vol. 60; no. 12; pp. 3310 - 3315
• Main Authors: Liu, Qingshan, Wang, Jun
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-12-2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: consensus; Convex functions; distributed optimization; Equations; Linear programming; Lyapunov function; Neurodynamics; Optimization; Recurrent neural networks; Second-order multi-agent network; Vectors; distributed optimization; second-order multi-agent network; Consensus; Lyapunov function
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2416927

This technical note presents a second-order multi-agent network for distributed optimization with a sum of convex objective functions subject to bound constraints. In the multi-agent network, the agents connect each others locally as an undirected graph and know only their own objectives and constraints. The multi-agent network is proved to be able to reach consensus to the optimal solution under mild assumptions. Moreover, the consensus of the multi-agent network is converted to the convergence of a dynamical system, which is proved using the Lyapunov method. Compared with existing multi-agent networks for optimization, the second-order multi-agent network herein is capable of solving more general constrained distributed optimization problems. Simulation results on two numerical examples are presented to substantiate the performance and characteristics of the multi-agent network.