A projection-based recurrent neural network and its application in solving convex quadratic bilevel optimization problems

In this paper, a projection-based recurrent neural network is proposed to solve convex quadratic bilevel programming problems (CQBPP). The Karush–Kuhn–Tucker optimal conditions (KKT) of the lower level problem are used to obtain identical one-level optimization problem. A projected dynamical system which its equilibrium point coincides with the global optimal solution of the corresponding optimization problem is presented. Compared to existing models, the proposed model has the least number of variables and a simple structure with low complexity. Analytically, it is demonstrated that the state vector of the suggested neural network model is stable in the sense of Lyapunov and globally convergent to an optimal solution of CQBPP in finite time. Some numerical examples, a supply chain model and an application deals with an environmental problem are discussed in order to confirm the efficiency of the theoretical results and the performance of the model.