http://dx.doi.org/10.1016/j.neucom.2012.01.020">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Efficient neural networks for solving variational inequalities

Language

English

Abstract

In this paper, we propose efficient neural network models for solving a class of variational inequality problems. Our first model can be viewed as a generalization of the basic projection neural network proposed by Friesz et al. [3]. As the basic projection neural network, it only needs some function evaluations and projections onto the constraint set, which makes the model very easy to implement, especially when the constraint set has some special structure such as a box, or a ball. Under the condition that the underlying mapping F is pseudo-monotone with respect to a solution, a condition that is much weaker than those required by the basic projection neural network, we prove the global convergence of the proposed neural network. If F is strongly pseudo-monotone, we prove its globally exponential stability. Then to improve the efficient of the neural network, we modify it by choosing a new direction that is bounded away from zero. Under the condition that the underlying mapping F is co-coercive, a condition that is a little stronger than pseudo-monotone but is still weaker than those required by the basic projection neural network, we prove the exponential stability and global convergence of the improved model. We also reported some computational results, which illustrated that the new method is more efficient than that of Friesz et al. [3]. © 2012 Elsevier B.V.

Keywords

Co-coercive mappings, Exponential stability, Projection neural networks, Pseudo-monotone mapping, Variational inequalities

Publication Date

2012

Source Publication Title

Neurocomputing

Volume

86

Issue

1

Start Page

97

End Page

106

Publisher

Elsevier

ISSN (print)

09252312

This document is currently not available here.

Share

COinS