Exponential convergence of a proximal projection neural network for mixed variational inequalities and applications

2021 ◽  
Author(s):  
Xingxing Ju ◽  
Hangjun Che ◽  
Chuandong Li ◽  
Xing He ◽  
Gang Feng
Keyword(s):  
Neural Network ◽  
Variational Inequalities ◽  
Exponential Convergence ◽  
Mixed Variational Inequalities ◽  
Projection Neural Network

An Inertial Projection Neural Network for Solving Variational Inequalities

2017 ◽  
Vol 47 (3) ◽  
pp. 809-814 ◽  
Author(s):  
Xing He ◽  
Tingwen Huang ◽  
Junzhi Yu ◽  
Chuandong Li ◽  
Chaojie Li
Keyword(s):  
Neural Network ◽  
Variational Inequalities ◽  
Projection Neural Network

On Exponential Convergence Conditions of an Extended Projection Neural Network

2008 ◽  
Vol 20 (9) ◽  
pp. 2227-2237 ◽  
Author(s):  
Youshen Xia ◽  
Dongyi Ye
Keyword(s):  
Neural Network ◽  
Variational Inequality ◽  
Jacobian Matrix ◽  
Exponential Convergence ◽  
Positive Semidefinite ◽  
Variational Inequality Problems ◽  
Nonlinear Mapping ◽  
Extended Projection ◽  
Monotone Variational Inequality ◽  
Projection Neural Network

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.

Sign in / Sign up

Export Citation Format

Share Document