title: On exponential convergence conditions of an extended projection neural network.
abstract: 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.
authors.affiliation: College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China. ysxia2001@yahoo.com
authors.forename: Youshen
authors.initials: Y
authors.lastname: Xia
authors.forename: Dongyi
authors.initials: D
authors.lastname: Ye
mesh_terms: D000818:Animals; D001931:Brain Mapping; D003198:Computer Simulation; D006801:Humans; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics