Neural networks for solving second-order cone constrained variational inequality problem

Juhe Sun, Jein Shan Chen, Chun Hsu Ko

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

In this paper, we consider using the neural networks to efficiently solve the second-order cone constrained variational inequality (SOCCVI) problem. More specifically, two kinds of neural networks are proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of the SOCCVI problem. The first neural network uses the Fischer-Burmeister (FB) function to achieve an unconstrained minimization which is a merit function of the Karush-Kuhn-Tucker equation. We show that the merit function is a Lyapunov function and this neural network is asymptotically stable. The second neural network is introduced for solving a projection formulation whose solutions coincide with the KKT triples of SOCCVI problem. Its Lyapunov stability and global convergence are proved under some conditions. Simulations are provided to show effectiveness of the proposed neural networks.

Original languageEnglish
Pages (from-to)623-648
Number of pages26
JournalComputational Optimization and Applications
Volume51
Issue number2
DOIs
Publication statusPublished - 2012 Mar 1

Keywords

  • Fischer-Burmeister function
  • Lyapunov stable
  • Neural network
  • Projection function
  • Second-order cone
  • Variational inequality

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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