A Neural Network for a Class of Horizontal Linear Complementary Problems

Based on the inherent properties of horizontal linear complementarity problems, this paper presents a neural network for solving a class of horizontal linear complementarity problem in real time by introducing the new vectors. Two sufficient conditions are provided to ensure that the proposed neural network is stable in the sense of Lyapunov and converges to an exact solution of the underlying problem. Furthermore, globally exponential stability of the proposed neural network is also shown under mild conditions. The proposed neural network has a one-layer structure and its size is only half of the original problem, and can be applied to some nonmonotone problems. The validity and transient behavior of the proposed neural network are illustrated by some simulation results.