A general projection neural network for solving monotone variational inequalities and related optimization problems

Youshen Xia, Jun Wang

Research output: Contribution to journalArticlepeer-review

248 Citations (Scopus)

Abstract

Recently, a projection neural network for solving monotone variational inequalities and constrained optimization problems was developed. In this paper, we propose a general projection neural network for solving a wider class of variational inequalities and related optimization problems. In addition to its simple structure and low complexity, the proposed neural network includes existing neural networks for optimization, such as the projection neural network, the primal-dual neural network, and the dual neural network, as special cases. Under various mild conditions, the proposed general projection neural network is shown to be globally convergent, globally asymptotically stable, and globally exponentially stable. Furthermore, several improved stability criteria on two special cases of the general projection neural network are obtained under weaker conditions. Simulation results demonstrate the effectiveness and characteristics of the proposed neural network.

Original languageEnglish
Pages (from-to)318-328
Number of pages11
JournalIEEE Transactions on Neural Networks
Volume15
Issue number2
DOIs
Publication statusPublished - Mar 2004
Externally publishedYes

Keywords

  • Global stability
  • Recurrent neural networks
  • Variational inequalities optimization

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