Clifford-Valued Distributed Optimization Based on Recurrent Neural Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 34; no. 10; pp. 7248 - 7259
• Main Authors: Xia, Zicong, Liu, Yang, Kou, Kit Ian, Wang, Jun
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.10.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algebra; Artificial neural networks; Clifford-valued distributed optimization; Clifford-valued neural networks; Computer science; Lyapunov theory; Neural networks; Neurodynamics; Neurons; nonsmooth analysis; Objective function; Optimization; Recurrent neural networks
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2021.3139865

In this paper, we address the Clifford-valued distributed optimization subject to linear equality and inequality constraints. The objective function of the optimization problems is composed of the sum of convex functions defined in the Clifford domain. Based on the generalized Clifford gradient, a system of multiple Clifford-valued recurrent neural networks (RNNs) is proposed for solving the distributed optimization problems. Each Clifford-valued RNN minimizes a local objective function individually, with local interactions with others. The convergence of the neural system is rigorously proved based on the Lyapunov theory. Two illustrative examples are delineated to demonstrate the viability of the results in this article.