Mathematical Programming: Series A and B
Mathematical Methods for Neural Network Analysis and Design
Mathematical Methods for Neural Network Analysis and Design
On Convergence Conditions of an Extended Projection Neural Network
Neural Computation
An Extended Projection Neural Network for Constrained Optimization
Neural Computation
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Recently the extended projection neural network was proposed to solve constrained monotone variational inequality problems and a class of constrained nonmonotontic variational inequality problems. Its exponential convergence was developed under the positive definiteness condition of the Jacobian matrix of the nonlinear mapping. This note proposes new results on the exponential convergence of the output trajectory of the extended projection neural network under the weak conditions that the Jacobian matrix of the nonlinear mapping may be positive semidefinite or not. Therefore, new results further demonstrate that the extended projection neural network has a fast convergence rate when solving a class of constrained monotone variational inequality problems and nonmonotonic variational inequality problems. Illustrative examples show the significance of the obtained results.