A 2D approach to tomographic image reconstruction using a Hopfield-type neural network
Artificial Intelligence in Medicine
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
Robust Model Predictive Control Using a Discrete-Time Recurrent Neural Network
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
A new projection-based neural network for constrained variational inequalities
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Real time identification and control of dynamic systems using recurrent neural networks
Artificial Intelligence Review
Information Sciences: an International Journal
The Projection Neural Network for Solving Convex Nonlinear Programming
ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
Solving convex optimization problems using recurrent neural networks in finite time
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
On a Stabilization Problem of Nonlinear Programming Neural Networks
Neural Processing Letters
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on game theory
Design of recurrent neural networks for solving constrained least absolute deviation problems
IEEE Transactions on Neural Networks
A new neural network for solving nonlinear programming problems
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Neural networks for solving second-order cone constrained variational inequality problem
Computational Optimization and Applications
Recurrent networks for compressive sampling
Neurocomputing
| Hi-index | 0.00 |
In recent years, a recurrent neural network called projection neural network was proposed for solving monotone variational inequalities and related convex optimization problems. In this paper, we show that the projection neural network can also be used to solve pseudomonotone variational inequalities and related pseudoconvex optimization problems. Under various pseudomonotonicity conditions and other conditions, the projection neural network is proved to be stable in the sense of Lyapunov and globally convergent, globally asymptotically stable, and globally exponentially stable. Since monotonicity is a special case of pseudomononicity, the projection neural network can be applied to solve a broader class of constrained optimization problems related to variational inequalities. Moreover, a new concept, called componentwise pseudomononicity, different from pseudomononicity in general, is introduced. Under this new concept, two stability results of the projection neural network for solving variational inequalities are also obtained. Finally, numerical examples show the effectiveness and performance of the projection neural network