Solving Variational Inequality Problems with Linear Constraints Based on a Novel Recurrent Neural Network

Authors:
Youshen Xia;Jun Wang
Affiliations:
College of Mathematics and Computer Science, Fuzhou University, China;Department of Automation and Computer-Aided Engineering, The Chinese, University of Hong Kong, China
Venue:
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
Year:
2007

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Abstract

Variational inequalities with linear inequality constraints are widely used in constrained optimization and engineering problems. By extending a new recurrent neural network [14], this paper presents a recurrent neural network for solving variational inequalities with general linear constraints in real time. The proposed neural network has one-layer projection structure and is amenable to parallel implementation. As a special case, the proposed neural network can include two existing recurrent neural networks for solving convex optimization problems and monotone variational inequality problems with box constraints, respectively. The proposed neural network is stable in the sense of Lyapunov and globally convergent to the solution under a monotone condition of the nonlinear mapping without the Lipschitz condition. Illustrative examples show that the proposed neural network is effective for solving this class of variational inequality problems.