New cooperative projection neural network for nonlinearly constrained variational inequality

This paper proposes a new cooperative projection neural network （CPNN）, which combines automatically three individual neural network models with a common projection term. As a special case, the proposed CPNN can include three recent recurrent neural networks for solving monotone variational inequality problems with limit or linear constraints, respectively. Under the monotonicity condition of the corresponding Lagrangian mapping, the proposed CPNN is theoretically guaranteed to solve monotone variational inequality problems and a class of nonmonotone variational inequality problems with linear and nonlinear constraints. Unlike the extended projection neural network, the proposed CPNN has no limitation on the initial point for global convergence. Compared with other related cooperative neural networks and numerical optimization algorithms, the proposed CPNN has a low computational complexity and requires weak convergence conditions. An application in real-time grasping force optimization and examples demonstrate good performance of the proposed CPNN.