A neural network for solving a convex quadratic bilevel programming problem (Q964970)

Bilevel programming (BLP) has increasingly been addressed in the literature both from the theoretical and computational points of view. It is well known that the neural network has become an important computing element, which can provide real-time optimal solutions for some practical optimization problems. Although there have been various types of analogous neural networks proposed for computation, there are only several reports on solving BLP problem using a neural network approach. Here, for the convex quadratic BLP problem, the authors propose a neural network that is globally and asymptotically stable. That means, based on Lyapunov and LaSalle theories that, for an arbitrary initial point, the trajectory of the proposed neural network converges to the equilibrium point, which is also an optimal solution of the convex quadratic BLP problem. Numerical simulation results show that the proposed neural network is feasible and efficient for a convex quadratic BLP problem.