A novel neural network for variational inequalities with linear and nonlinear constraints

Xing Bao Gao, Li Zhi Liao, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

58 Citations (Scopus)


Variational inequality is a uniform approach for many important optimization and equilibrium problems. Based on the sufficient and necessary conditions of the solution, this paper presents a novel neural network model for solving variational inequalities with linear and nonlinear constraints. Three sufficient conditions are provided to ensure that the proposed network with an asymmetric mapping is stable in the sense of Lyapunov and converges to an exact solution of the original problem. Meanwhile, the proposed network with a gradient mapping is also proved to be stable in the sense of Lyapunov and to have a finite-time convergence under some mild conditions by using a new energy function. Compared with the existing neural networks, the new model can be applied to solve some nonmonotone problems, has no adjustable parameter, and has lower complexity. Thus, the structure of the proposed network is very simple. Since the proposed network can be used to solve a broad class of optimization problems, it has great application potential. The validity and transient behavior of the proposed neural network are demonstrated by several numerical examples.
Original languageEnglish
Pages (from-to)1305-1317
Number of pages13
JournalIEEE Transactions on Neural Networks
Issue number6
Publication statusPublished - 1 Nov 2005


  • Convergence
  • Neural network
  • Stability
  • Variational inequality

ASJC Scopus subject areas

  • Software
  • General Medicine
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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