A recurrent neural network with finite-time convergence for convex quadratic bilevel programming problems

Abstract

In this paper, a recurrent neural network with a new tunable activation is proposed to solve a kind of convex quadratic bilevel programming problem. It is proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov, and the state of the proposed neural network converges to an equilibrium point in finite time. In contrast to the existing related neurodynamic approaches, the proposed neural network in this paper is capable of solving the convex quadratic bilevel programming problem in finite time. Moreover, the finite convergence time can be quantitatively estimated. Finally, two numerical examples are presented to show the effectiveness of the proposed recurrent neural network.