A neural network for the linear complementarity problem

An artificial neural network is proposed in this paper for solving the line ar complementarity problem. The new neural network is based on a reformulat ion of the linear complementarity problem into the unconstrained minimizati on problem. Our new neural network can be easily implemented on a circuit. On the theoretical aspect, we analyze the existence of the equilibrium poin ts for our neural network. In addition, we prove that if the equilibrium po int exists for the neural network, then any such equilibrium point is both asymptotically and bounded (Lagrange) stable for any initial state. Further more, linear programming and certain quadratical programming problems (not necessarily convex) can be also solved by the neural network. Simulation re sults on several problems including a nonconvex one are also reported. (C) 1999 Elsevier Science Ltd. All rights reserved.