Convergence of the Projection-Based Generalized Neural Network and the Application to Nonsmooth Optimization Problems

This paper introduces a projection-based generalized neural network, which can be used to solve a class of nonsmooth convex optimization problems It generalizes the existing projection neural networks for solving the optimization problems In addition, the existence and convergence of the solution for the generalized neural networks are proved Moreover, we discuss the application to nonsmooth convex optimization problems And two illustrative examples are given to show the efficiency of the theoretical results.

[1]  Gang Feng,et al.  A new neural network for solving nonlinear projection equations , 2007, Neural Networks.

[2]  Mauro Forti,et al.  Convergence of Neural Networks for Programming Problems via a Nonsmooth Łojasiewicz Inequality , 2006, IEEE Transactions on Neural Networks.

[4]  Sanqing Hu,et al.  A Recurrent Neural Network for Non-smooth Nonlinear Programming Problems , 2007, 2007 International Joint Conference on Neural Networks.

[5]  Li-Zhi Liao,et al.  A New Projection-Based Neural Network for Constrained Variational Inequalities , 2009, IEEE Transactions on Neural Networks.

[6]  Gang Feng,et al.  On Convergence Conditions of an Extended Projection Neural Network , 2005, Neural Computation.

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

[8]  Mauro Forti,et al.  Generalized neural network for nonsmooth nonlinear programming problems , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Muhammad Aslam Noor,et al.  Some new projection methods for variational inequalities , 2003, Appl. Math. Comput..

[10]  Jinde Cao,et al.  A delayed neural network for solving linear projection equations and its analysis , 2005, IEEE Transactions on Neural Networks.

[11]  Qingshan Liu,et al.  A One-Layer Recurrent Neural Network With a Discontinuous Hard-Limiting Activation Function for Quadratic Programming , 2008, IEEE Transactions on Neural Networks.

[12]  Jinde Cao,et al.  A Delayed Neural Network Method for Solving Convex Optimization Problems , 2006, Int. J. Neural Syst..

[13]  Jun Wang,et al.  Convergence Analysis of a Class of Nonsmooth Gradient Systems , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Qingshan Liu,et al.  A One-Layer Recurrent Neural Network with a Discontinuous Activation Function for Linear Programming , 2008, Neural Computation.

[15]  Jean-Pierre Aubin,et al.  Viability theory , 1991 .

[16]  Wei Bian,et al.  Subgradient-Based Neural Networks for Nonsmooth Nonconvex Optimization Problems , 2009, IEEE Transactions on Neural Networks.

[17]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[18]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[19]  Wei Bian,et al.  Subgradient-Based Neural Networks for Nonsmooth Convex Optimization Problems , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.