Department of Mathematics
A novel neural network for generally constrained variational inequalities
This paper presents a novel neural network for solving generally constrained variational inequality problems by constructing a system of double projection equations. By defining proper convex energy functions, the proposed neural network is proved to be stable in the sense of Lyapunov and converges to an exact solution of the original problem for any starting point under the weaker cocoercivity condition or the monotonicity condition of the gradient mapping on the linear equation set. Furthermore, two sufficient conditions are provided to ensure the stability of the proposed neural network for a special case. The proposed model overcomes some shortcomings of existing continuous-time neural networks for constrained variational inequality, and its stability only requires some monotonicity conditions of the underlying mapping and the concavity of nonlinear inequality constraints on the equation set. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.
Neural networks, Stability analysis, Asymptotic stability, Mathematical model, Computational modeling, Real-time systems, Optimization
Source Publication Title
IEEE Transactions on Neural Networks and Learning Systems
Institute of Electrical and Electronics Engineers
This work was supported in part by National Natural Science Foundation of China, under Grant 61273311 and Grant 61173094, in part by the Faculty Research Fund, Hong Kong Baptist University, and in part by the General Research Fund, Hong Kong.
Link to Publisher's Edition
Gao, X., & Liao, L. (2016). A novel neural network for generally constrained variational inequalities. IEEE Transactions on Neural Networks and Learning Systems, PP (99), 1-14. https://doi.org/10.1109/TNNLS.2016.2570257