A neural network for a generalized vertical complementarity problem

In this paper, an efficient artificial neural network is proposed for solving a generalized vertical complementarity problem. Based on the properties of log-exponential function, the generalized vertical complementarity problem is reformulated in terms of the unconstrained minimization problem. The existence and the convergence of the trajectory of the neural network are addressed in detail. In addition, it is also proved that if the neural network problem has an equilibrium point under some initial condition, the equilibrium point is asymptotically stable or exponentially stable under certain conditions. At the end of this paper, the simulation results for the generalized bimatrix game are illustrated to show the efficiency of the neural network.