Efficient neural networks for solving variational inequalities

Suoliang Jiang, Deren Han*, Xiaoming YUAN

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

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].

Original languageEnglish
Pages (from-to)97-106
Number of pages10
JournalNeurocomputing
Volume86
DOIs
Publication statusPublished - 1 Jun 2012

Scopus Subject Areas

  • Computer Science Applications
  • Cognitive Neuroscience
  • Artificial Intelligence

User-Defined Keywords

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

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