A neural network for the linear complementarity problem

Li-Zhi Liao*, Hou-Duo Qi

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

28 Citations (Scopus)


An artificial neural network is proposed in this paper for solving the linear complementarity problem. The new neural network is based on a reformulation of the linear complementarity problem into the unconstrained minimization problem. Our new neural network can be easily implemented on a circuit. On the theoretical aspect, we analyze the existence of the equilibrium points for our neural network. In addition, we prove that if the equilibrium point exists for the neural network, then any such equilibrium point is both asymptotically and bounded (Lagrange) stable for any initial state. Furthermore, linear programming and certain quadratical programming problems (not necessarily convex) can be also solved by the neural network. Simulation results on several problems including a nonconvex one are also reported.

Original languageEnglish
Pages (from-to)9-18
Number of pages10
JournalMathematical and Computer Modelling
Issue number3
Publication statusPublished - Feb 1999

Scopus Subject Areas

  • Modelling and Simulation
  • Computer Science Applications

User-Defined Keywords

  • Neural network
  • Linear complementarity problem
  • Stability


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