An RNN-Based Algorithm for Decentralized-Partial-Consensus Constrained Optimization

• Published in: IEEE transaction on neural networks and learning systems Vol. 34; no. 1; pp. 534 - 542
• Main Authors: Xia, Zicong, Liu, Yang, Qiu, Jianlong, Ruan, Qihua, Cao, Jinde
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Constraints; Cost function; Decentralized-partial-consensus optimization (DPCO); Learning systems; Neural networks; Neurodynamics; nonsmooth analysis; Optimization; Optimization methods; partial-consensus matrix; Recurrent neural networks; recurrent neural networks (RNNs); Task analysis
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2021.3098668

This technical note proposes a decentralized-partial-consensus optimization (DPCO) problem with inequality constraints. The partial-consensus matrix originating from the Laplacian matrix is constructed to tackle the partial-consensus constraints. A continuous-time algorithm based on multiple interconnected recurrent neural networks (RNNs) is derived to solve the optimization problem. In addition, based on nonsmooth analysis and Lyapunov theory, the convergence of continuous-time algorithm is further proved. Finally, several examples demonstrate the effectiveness of main results.