A recurrent neural network for solving linear projection equations

Youshen Xia, Jun Wang

Research output: Contribution to journalArticlepeer-review

132 Citations (Scopus)

Abstract

Linear projection equations arise in many optimization problems and have important applications in science and engineering. In this paper, we present a recurrent neural network for solving linear projection equations in real time. The proposed neural network has two layers and is amenable to parallel implementation with simple hardware. In the theoretical aspect, we prove that the proposed neural network can converge globally to the solution set of the problem when the matrix involved in the problem is positive semidefinite and can converge exponentially to a unique solution when the matrix is positive definite. In addition, we analyze the stability of the related dynamic system in detail. As an application, we show that the proposed neural network can be used directly to solve linear and convex quadratic programming problems and linear complementary problems with positive semidefinite matrices. The validity and transient behavior of the neural network are demonstrated by using three numerical examples. Copyright (C) 2000 Elsevier Science Ltd.

Original languageEnglish
Pages (from-to)337-350
Number of pages14
JournalNeural Networks
Volume13
Issue number3
DOIs
Publication statusPublished - Apr 2000
Externally publishedYes

Keywords

  • Convergence
  • Linear projection equations
  • Recurrent neural networks

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