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

Abstract

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.