Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network

• Published in: IEEE transactions on neural networks Vol. 17; no. 6; pp. 1487 - 1499
• Main Authors: Hu, Xiaolin, Wang, Jun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2006; Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Artificial neural networks; Asymptotic properties; Asymptotic stability; Circuits; Componentwise pseudomonotone variational inequality; Computer science; control theory; systems; Connectionism. Neural networks; Constraint optimization; Constraints; Convergence; Exact sciences and technology; global asymptotic stability; Inequalities; Information Storage and Retrieval - methods; Iterative algorithms; Neural networks; Neural Networks (Computer); Optimization; Pattern Recognition, Automated - methods; Projection; projection neural network; pseudoconvex optimization; pseudomonotone variational inequality; Recurrent neural networks; Signal processing algorithms; Signal Processing, Computer-Assisted; Stability; Telecommunication traffic; Monotonic function; Recurrent neural nets; Componentwise pseudomonotone variational inequality; global asymptotic stability; pseudoconvex optimization; Lyapunov method; Neural network; Convex programming; Constrained optimization; projection neural network; Asymptotic stability; Variational inequality; pseudomonotone variational inequality; Monotonicity; Lyapunov function; Mathematical programming
• ISSN: 1045-9227; 1941-0093
• DOI: 10.1109/TNN.2006.879774

In recent years, a recurrent neural network called projection neural network was proposed for solving monotone variational inequalities and related convex optimization problems. In this paper, we show that the projection neural network can also be used to solve pseudomonotone variational inequalities and related pseudoconvex optimization problems. Under various pseudomonotonicity conditions and other conditions, the projection neural network is proved to be stable in the sense of Lyapunov and globally convergent, globally asymptotically stable, and globally exponentially stable. Since monotonicity is a special case of pseudomononicity, the projection neural network can be applied to solve a broader class of constrained optimization problems related to variational inequalities. Moreover, a new concept, called componentwise pseudomononicity, different from pseudomononicity in general, is introduced. Under this new concept, two stability results of the projection neural network for solving variational inequalities are also obtained. Finally, numerical examples show the effectiveness and performance of the projection neural network