Distributed nonconvex optimization subject to globally coupled constraints via collaborative neurodynamic optimization

• Published in: Neural networks Vol. 184; p. 107027
• Main Authors: Xia, Zicong, Liu, Yang, Hu, Cheng, Jiang, Haijun
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.04.2025
• Subjects: Algorithms; Augmented Lagrangian function; Collaborative neurodynamic optimization; Computer Simulation; Distributed nonconvex optimization; Humans; Neural Networks, Computer; Recurrent neural network; Distributed nonconvex optimization; Collaborative neurodynamic optimization; Augmented Lagrangian function; Recurrent neural network
• ISSN: 0893-6080; 1879-2782; 1879-2782
• DOI: 10.1016/j.neunet.2024.107027

In this paper, a recurrent neural network is proposed for distributed nonconvex optimization subject to globally coupled (in)equality constraints and local bound constraints. Two distributed optimization models, including a resource allocation problem and a consensus-constrained optimization problem, are established, where the objective functions are not necessarily convex, or the constraints do not guarantee a convex feasible set. To handle the nonconvexity, an augmented Lagrangian function is designed, based on which a recurrent neural network is developed for solving the optimization models in a distributed manner, and the convergence to a local optimal solution is proven. For the search of global optimal solutions, a collaborative neurodynamic optimization method is established by utilizing multiple proposed recurrent neural networks and a meta-heuristic rule. A numerical example, a simulation involving an electricity market, and a distributed cooperative control problem are provided to verify and demonstrate the characteristics of the main results.