Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Foundations of robotics: analysis and control
Foundations of robotics: analysis and control
Neural networks for signal processing
Neural networks for signal processing
A globally convergent Newton method for solving strongly monotone variational inequalities
Mathematical Programming: Series A and B
Modified Projection-Type Methods for Monotone Variational Inequalities
SIAM Journal on Control and Optimization
A class of iterative methods for solving nonlinear projection equations
Journal of Optimization Theory and Applications
On the stability of globally projected dynamical systems
Journal of Optimization Theory and Applications
Improvements of some projection methods for monotone nonlinear variational inequalities
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
A novel neural network for a class of convex quadratic minimax problems
Neural Computation
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
A new modified Goldstein-Levitin-Polyakprojection method for variational inequality problems
Computers & Mathematics with Applications
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on game theory
IEEE Transactions on Neural Networks
A note on a globally convergent Newton method for solving monotone variational inequalities
Operations Research Letters
A general methodology for designing globally convergent optimization neural networks
IEEE Transactions on Neural Networks
A neural network model for monotone linear asymmetric variational inequalities
IEEE Transactions on Neural Networks
Exponential stability of globally projected dynamic systems
IEEE Transactions on Neural Networks
A novel neural network for nonlinear convex programming
IEEE Transactions on Neural Networks
A novel neural network for variational inequalities with linear and nonlinear constraints
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
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In this paper, we propose efficient neural network models for solving a class of variational inequality problems. Our first model can be viewed as a generalization of the basic projection neural network proposed by Friesz et al. [3]. As the basic projection neural network, it only needs some function evaluations and projections onto the constraint set, which makes the model very easy to implement, especially when the constraint set has some special structure such as a box, or a ball. Under the condition that the underlying mapping F is pseudo-monotone with respect to a solution, a condition that is much weaker than those required by the basic projection neural network, we prove the global convergence of the proposed neural network. If F is strongly pseudo-monotone, we prove its globally exponential stability. Then to improve the efficient of the neural network, we modify it by choosing a new direction that is bounded away from zero. Under the condition that the underlying mapping F is co-coercive, a condition that is a little stronger than pseudo-monotone but is still weaker than those required by the basic projection neural network, we prove the exponential stability and global convergence of the improved model. We also reported some computational results, which illustrated that the new method is more efficient than that of Friesz et al. [3].