论文信息 - Three Global Exponential Convergence Results of the GPNN for Solving Generalized Linear Variational Inequalities

Three Global Exponential Convergence Results of the GPNN for Solving Generalized Linear Variational Inequalities

The general projection neural network (GPNN) is a versatile recurrent neural network model capable of solving a variety of optimization problems and variational inequalities. In a recent article [IEEE Trans. Neural Netw., 18(6), 1697-1708, 2007], the linear case of GPNN was studied extensively from the viewpoint of stability analysis, and it was utilized to solve the generalized linear variational inequality with various types of constraints. In the present paper we supplement three global exponential convergence results for the GPNN for solving these problems. The first one is different from those shown in the original article, and the other two are improved versions of two results in that article. The validity of the new results are demonstrated by numerical examples.

Zhigang Zeng | Xiaolin Hu | Bo Zhang

[1] Jun Wang,et al. A general projection neural network for solving monotone variational inequalities and related optimization problems , 2004, IEEE Transactions on Neural Networks.

[2] Xiaolin Hu,et al. Applications of the general projection neural network in solving extended linear-quadratic programming problems with linear constraints , 2009, Neurocomputing.

[3] Xiaolin Hu,et al. Design of General Projection Neural Networks for Solving Monotone Linear Variational Inequalities and Linear and Quadratic Optimization Problems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4] Gang Feng,et al. Development and Analysis of a Neural Dynamical Approach to Nonlinear Programming Problems , 2007, IEEE Transactions on Automatic Control.

[5] Jun Wang,et al. Global exponential stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[6] Bingsheng He. Solution and applications of a class of general linear variational inequalities , 1996 .

[7] Xiaolin Hu,et al. Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks , 2007, IEEE Transactions on Neural Networks.