Penalty-Function-Type Multi-Agent Approaches to Distributed Nonconvex Optimal Resource Allocation

• Published in: IEEE transactions on network science and engineering Vol. 11; no. 5; pp. 4169 - 4180
• Main Authors: Xia, Zicong, Yu, Wenwu, Liu, Yang, Jia, Wenwen, Chen, Guanrong
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.09.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Air conditioning; Communication networks; Constraints; Distributed optimal resource allocation; Functional analysis; Heating systems; HVAC; Lagrangian function; Lagrangian functions; Linear programming; Mathematical models; multi-agent system; Multi-agent systems; Multiagent systems; networked optimization; nonconvex optimization; Optimal control; Optimization; penalty function method; Resource allocation; Resource management; Ventilation
• ISSN: 2327-4697; 2334-329X
• DOI: 10.1109/TNSE.2024.3401748

In this paper, a class of penalty-function-type multi-agent approaches via communication networks is developed for distributed nonconvex optimal resource allocation. A penalty-function-type method is utilized to handle networked resource allocation constraints, and a multi-agent method is employed for handling global information in a distributed manner. Then, a penalty-function-type multi-agent system is constructed for a nonconvex optimal resource allocation model, and its stability with a local minimizer is proven. Further, a nonconvex optimal resource allocation model subject to "on/off" constraints is introduced. Based on an augmented Lagrangian function, another penalty-function-type multi-agent system is developed, and it is proven to be stable with a local minimizer. A numerical example with simulation in a heating, ventilation, and air conditioning system is presented to demonstrate the theoretical results.