论文信息 - A New Delayed Projection Neural Network for Solving Linear Variational Inequalities and Quadratic Optimization Problems

A New Delayed Projection Neural Network for Solving Linear Variational Inequalities and Quadratic Optimization Problems

For solving linear variational inequalities(LVIs) and quadratic optimization problems(QOPs), a new delayed projection neural network is proposed in this paper. And some sufficient conditions ensuring exponential stability are obtained via constructing appropriate Lyapunov functionals. As a special case, a matrix constraint is considered too. In this case, by dividing the network state variables into subgroups according to the character of the activation functions, some more compact sufficient conditions ensuring exponential stability are obtained, and these conditions are only relate to some blocks of the interconnection matrix. One numerical example will be presented, to show the effectiveness of the main results.

[1] F. Facchinei,et al. Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

[2] 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).

[3] Jinde Cao,et al. A feedback neural network for solving convex constraint optimization problems , 2008, Appl. Math. Comput..

[4] N. Huang,et al. A new class of interval projection neural networks for solving interval quadratic program , 2008 .

[5] S. Zhong,et al. Exponential stability of neural networks with asymmetric connection weights , 2007 .

[6] Patrick T. Harker,et al. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[7] Xinzhi Liu,et al. Exponential stability and periodicity of cellular neural networks with time delay , 2007, Math. Comput. Model..

[8] Heng-you Lan. An approach for solving fuzzy implicit variational inequalities with linear membership functions , 2008, Comput. Math. Appl..

[9] Alaeddin Malek,et al. Solving complementarity and variational inequalities problems using neural networks , 2007, Appl. Math. Comput..

[10] C. Baiocchi,et al. Variational and quasivariational inequalities: Applications to free boundary problems , 1983 .