Neural network for solving Nash equilibrium problem in application of multiuser power control

In this paper, based on an equivalent mixed linear complementarity problem, we propose a neural network to solve multiuser power control optimization problems (MPCOP), which is modeled as the noncooperative Nash game in modern digital subscriber line (DSL). If the channel crosstalk coefficients matrix is positive semidefinite, it is shown that the proposed neural network is stable in the sense of Lyapunov and global convergence to a Nash equilibrium, and the Nash equilibrium is unique if the channel crosstalk coefficients matrix is positive definite. Finally, simulation results on two numerical examples show the effectiveness and performance of the proposed neural network.