One-Layer Continuous-and Discrete-Time Projection Neural Networks for Solving Variational Inequalities and Related Optimization Problems

• Published in: IEEE transaction on neural networks and learning systems Vol. 25; no. 7; pp. 1308 - 1318
• Main Authors: Liu, Qingshan, Huang, Tingwen, Wang, Jun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Connectionism. Neural networks; Constrained optimization; Convergence; Educational institutions; Exact sciences and technology; global convergence; Lyapunov methods; Lyapunov stability; Mathematical model; Neural networks; Optimization; projection neural network; variational inequalities; Vectors; projection neural network; Lyapunov stability; variational inequalities; global convergence; Constrained optimization; Stability; Lyapunov method; Continuous time; Neural network; Projection method; Projection operator; Variational inequality; Discrete time; Lyapunov function; Mathematical programming
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2013.2292893

This paper presents one-layer projection neural networks based on projection operators for solving constrained variational inequalities and related optimization problems. Sufficient conditions for global convergence of the proposed neural networks are provided based on Lyapunov stability. Compared with the existing neural networks for variational inequalities and optimization, the proposed neural networks have lower model complexities. In addition, some improved criteria for global convergence are given. Compared with our previous work, a design parameter has been added in the projection neural network models, and it results in some improved performance. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural networks.