A neural network for the linear complementarity problem

Abstract

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.