A Continuous Finite-time Neural Network with Bias Noises for Convex Quadratic Bilevel Programming Problem

A continuous finite-time neural network with bias noises is proposed to solve the convex quadratic bilevel programming problem in this paper. In order to solve the convex quadratic bilevel programming problem, it is transformed into a nonlinear programming problem based on the Kaeush-Kuhn-Tucker conditions. Then, a neural network is designed to solve this problem. Compared with the existing networks, the designed network contains biased noise. Furthermore, it is proved that the proposed neural network can converge to the equilibrium point in finite time and it is Lyapunov stable. Moreover, the robustness performance of the present neural network against bias noises is discussed and the effect is very good. At the same time, the upper bound of the steady-state error is estimated. Lastly, two numerical examples show the effectiveness of the proposed methods.