Description:
In this paper, a feedback neural network model is proposed for solving a class of convex quadratic bi-level programming problems based on the idea of successive approximation. Differing from existing neural network models, the proposed neural network has the least number of state variables and simple structure. Based on Lyapunov theories, we prove that the equilibrium point sequence of the feedback neural network can approximately converge to an optimal solution of the convex quadratic bi-level problem under certain conditions, and the corresponding sequence of the function value approximately converges to the optimal value of the convex quadratic bi-level problem. Simulation experiments on three numerical examples and a portfolio selection problem are provided to show the effi- ciency and performance of the proposed neural network approach.
Description:
In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.
Description:
In this brief, considering the inertial term into first order neural networks(NNs), an inertial NN(INN) modeled by means of a differential inclusion is proposed for solving linear complementarity problem with P-0 matrix. Compared with existing NNs, the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different optimal solution. It is proved that the proposed NN is stable in the sense of Lyapunov and any equilibrium of our NN is the optimal solution of LCP with P-0 matrix. Simulation results on two numerical examples show the effectiveness and performance of the proposed neural network.