Mathematical Programming: Series A and B
Descent approaches for quadratic bilevel programming
Journal of Optimization Theory and Applications
On the resolution of monotone complementarity problems
Computational Optimization and Applications
Differential Inclusions: Set-Valued Maps and Viability Theory
Differential Inclusions: Set-Valued Maps and Viability Theory
A Global Optimization Method for Solving Convex Quadratic Bilevel Programming Problems
Journal of Global Optimization
A neural network approach for solving nonlinear bilevel programming problem
Computers & Mathematics with Applications
Computers & Mathematics with Applications
A neural network approach to multiobjective and multilevel programming problems
Computers & Mathematics with Applications
A neural network approach for solving linear bilevel programming problem
Knowledge-Based Systems
A neural network for solving a convex quadratic bilevel programming problem
Journal of Computational and Applied Mathematics
Journal of Global Optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A novel neural network for variational inequalities with linear and nonlinear constraints
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Neural network for solving linear programming problems with bounded variables
IEEE Transactions on Neural Networks
A One-Layer Recurrent Neural Network for Constrained Nonsmooth Optimization
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.