A Collaborative Neurodynamic Optimization Approach to Distributed Nash-Equilibrium Seeking in Multicluster Games With Nonconvex Functions

• Published in: IEEE transactions on cybernetics Vol. 54; no. 5; pp. 3105 - 3119
• Main Authors: Xia, Zicong, Liu, Yang, Yu, Wenwu, Wang, Jun
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.05.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Collaboration; Collaborative neurodynamic optimization (CNO); Convergence; distributed Nash-equilibrium seeking; Game theory; Games; Global optimization; Heuristic methods; Lagrangian function; Metaheuristics; multicluster game; Neurodynamics; nonconvexity; Optimization; Recurrent neural networks; recurrent neural networks (RNNs)
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2023.3289712

In this article, we propose a collaborative neurodynamic optimization (CNO) method for the distributed seeking of generalized Nash equilibriums (GNEs) in multicluster games with nonconvex functions. Based on an augmented Lagrangian function, we develop a projection neural network for the local search of GNEs, and its convergence to a local GNE is proven. We formulate a global optimization problem to which a global optimal solution is a high-quality local GNE, and we adopt a CNO approach consisting of multiple recurrent neural networks for scattering searches and a metaheuristic rule for reinitializing states. We elaborate on an example of a price-bidding problem in an electricity market to demonstrate the viability of the proposed approach.