A new projection-based neural network for constrained variational inequalities

Authors:
Xing-Bao Gao;Li-Zhi Liao
Affiliations:
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi, China;Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, China
Venue:
IEEE Transactions on Neural Networks
Year:
2009

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Abstract

This paper presents a new neural network model for solving constrained variational inequality problems by converting the necessary and sufficient conditions for the solution into a system of nonlinear projection equations. Five sufficient conditions are provided to ensure that the proposed neural network is stable in the sense of Lyapunov and converges to an exact solution of the original problem by defining a proper convex energy function. The proposed neural network includes an existing model, and can be applied to solve some nonmonotone and nonsmooth problems. The validity and transient behavior of the proposed neural network are demonstrated by some numerical examples.